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## Bibliography

1
  Agarwal, P. K., and Procopiuc, C. M. (1998),
  ``Exact and approximation algorithms for clustering'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 658-667.
  (MINIMUM K-CENTER)

2
  Agarwal, P. K., and Suri, S. (1994),
  ``Surface approximation and geometric partitions'',
  Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 34-43.
  (MINIMUM RED-BLUE SEPARATION)

3
  Agarwala, R., Bafna, V., Farach, M., Narayanan, B., Paterson, M., and Thorup, M. (1996),
  ``On the approximability of numerical taxonomy'',
  Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 365-372.
  (MINIMUM NUMERICAL TAXONOMY)

4
  Aggarwal, A., Coppersmith, D., Khanna, S., Motwani, R., and Schieber, B. (1997),
  ``The angular-metric traveling salesman problem'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 221-229.
  (MINIMUM GEOMETRIC TRAVELING SALESPERSON)

5
  Aggarwal, M., and Garg, N. (1994),
  ``A scaling technique for better network design'',
  Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 233-239.
  (MINIMUM GENERALIZED STEINER NETWORK)

6
  Akutsu, T., and Halldórsson, M. (1994),
  ``On the approximation of largest common point sets and largest common subtrees'',
  Proc. 5th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 834, Springer-Verlag, 405-413.
  (MAXIMUM COMMON SUBTREE, MAXIMUM COMMON POINT SET)

7
  Akutsu, T., and Halldórsson, M. (1997),
  ``On the approximation of largest common point sets and largest common subtrees'',
  Unpublished manuscript.
  (MAXIMUM COMMON SUBTREE)

8
  Alekhnovich, M., Buss, S., Moran, S., and Pitassi, T. (1998),
  ``Minimum propositional proof length is NP-hard to linearly approximate'',
  Proc. 23rd International Symp. on Mathematical Foundations of Comput. Sci., Lecture Notes in Comput. Sci. 1450, Springer-Verlag, 176-184.
  (MINIMUM LENGTH EQUIVALENT FREGE PROOF)

9
  Alimonti, P., and Kann, V. (1997),
  ``Hardness of approximating problems on cubic graphs'',
  Proc. 3rd Italian Conf. on Algorithms and Complexity, Lecture Notes in Comput. Sci. 1203, Springer-Verlag, 288-298.
  (MINIMUM VERTEX COVER, MAXIMUM CUT)

10
  Alon, N., Azar, Y., Woeginger, G. J., and Yadid, T. (1997),
  ``Approximation schemes for scheduling'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 493-500.
  (MINIMUM PARALLEL PROCESSOR TOTAL FLOW TIME)

11
  Alon, N., Csirik, J., Sevastianov, S. V., Vestjens, A. P. A., and Woeginger, G. J. (1996),
  ``On-line and off-line approximation algorithms for vector covering problems'',
  Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 406-418.
  (MAXIMUM D-VECTOR COVERING)

12
  Alon, N., Feige, U., Wigderson, A., and Zuckerman, D. (1995),
  ``Derandomized graph products'',
  Computational Complexity 5, 60-75.
  (MAXIMUM INDEPENDENT SET)

13
  Alon, N., and Kahale, N. (1994),
  ``Approximating the independence number via the -function'',
  Unpublished manuscript.
  (MAXIMUM CLIQUE, MAXIMUM INDEPENDENT SET)

14
  Alon, N., Yuster, R., and Zwick, U. (1994),
  ``Color-coding: a new method for finding simple paths, cycles and other small subgraphs within large graphs'',
  Proc. 26th Ann. ACM Symp. on Theory of Comp., ACM, 326-335.
  (LONGEST PATH)

15
  Amaldi, E., and Kann, V. (1995),
  ``The complexity and approximability of finding maximum feasible subsystems of linear relations'',
  Theoretical Comput. Sci. 147, 181-210.
  (MAXIMUM SATISFYING LINEAR SUBSYSTEM, MAXIMUM HYPERPLANE CONSISTENCY, MAXIMUM SATISFIABILITY OF QUADRATIC EQUATIONS OVER GF[Q])

16
  Amaldi, E., and Kann, V. (1998),
  ``On the approximability of minimizing nonzero variables or unsatisfied relations in linear systems'',
  Theoretical Comput. Sci. 209, 237-260.
  (MINIMUM RELEVANT VARIABLES IN LINEAR SYSTEM, MINIMUM UNSATISFYING LINEAR SUBSYSTEM, MAXIMUM HYPERPLANE CONSISTENCY)

17
  Amoura, A. K., Bampis, E., Kenyon, C., and Manoussakis, Y. (1997),
  ``How to schedule independent multiprocessor tasks'',
  Proc. 5th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1284, Springer-Verlag, 1-12.
  (MINIMUM 3-DEDICATED PROCESSOR SCHEDULING)

18
  Andersson, G. (1999),
  ``An approximation algorithm for MAX p-SECTION'',
  Proc. 16th Ann. Symp. on Theoretical Aspects of Comput. Sci., , Lecture Notes in Comput. Sci., Springer-Verlag, to appear.
  (MAXIMUM K-CUT)

19
  Andersson, G., and Engebretsen, L. (1998a),
  ``Better approximation algorithms for SET SPLITTING and NOT-ALL-EQUAL SAT'',
  Inform. Process. Lett. 65, 305-311.
  (MAXIMUM SET SPLITTING, MAXIMUM NOT-ALL-EQUAL 3-SATISFIABILITY)

20
  Andersson, G., and Engebretsen, L. (1998b),
  ``Sampling methods applied to non-boolean optimization problems'',
  Proc. 2nd Symp. on Randomization and Approximation Techniques in Comput. Sci., Lecture Notes in Comput. Sci. 1518, Springer-Verlag, 357-368.
  (MAXIMUM SATISFYING LINEAR SUBSYSTEM, MAXIMUM K-CONSTRAINT SATISFACTION)

21
  Andersson, G., Engebretsen, L., and Håstad, J. (1999),
  ``A new way to use semidefinite programming with applications to linear equations mod p'',
  Proc. 10th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 41-50.
  (MAXIMUM SATISFYING LINEAR SUBSYSTEM)

22
  Andreae, T., and Bandelt, H. (1995),
  ``Performance guarantees for approximation algorithms depending on parametrized triangle inequalities'',
  SIAM J. Disc. Math. 8, 1-16.
  (MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

23
  Anily, A., Bramel, J., and Simchi-Levi, D. (1994),
  ``Worst-case analysis of heuristics for the bin-packing problem with general cost structures'',
  Oper. Res. 42, 287-298.
  (MINIMUM BIN PACKING)

24
  Anily, S., and Hassin, R. (1992),
  ``The swapping problem'',
  Networks 22, 419-433.
  (MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

25
  Arkin, E. M., Chiang, Y., Mitchell, J. S. B., Skiena, S. S., and Yang, T. (1997),
  ``On the maximum scatter TSP'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 211-220.
  (MINIMUM METRIC BOTTLENECK WANDERING SALESPERSON PROBLEM)

26
  Arkin, E. M., Halldórsson, M. M., and Hassin, R. (1993),
  ``Approximating the tree and tour covers of a graph'',
  Inform. Process. Lett. 47, 275-282.
  (MINIMUM VERTEX COVER)

27
  Arkin, E. M., and Hassin, R. (1992),
  ``Multiple-choice minimum diameter problems'',
  Unpublished manuscript.
  (MINIMUM SET COVER)

28
  Arkin, E. M., and Hassin, R. (1994),
  ``Approximation algorithms for the geometric covering salesman problem'',
  Disc. Appl. Math. 55, 197-218.
  (MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

29
  Arkin, E. M., and Hassin, R. (1998),
  ``On local search for weighted packing probems'',
  Math. Oper. Res. 23, 640-648.
  (MAXIMUM 3-DIMENSIONAL MATCHING, MAXIMUM SET PACKING)

30
  Armen, C., and Stein, C. (1994),
  ``A 2-approximation algorithm for the shortest superstring problem'',
  Technical Report PCS-TR94-214, Department of Computer Science, Dartmouth College, Hanover, New Hampshire.
  (SHORTEST COMMON SUPERSTRING)

31
  Arora, S. (1996),
  ``Polynomial time approximation scheme for Euclidean TSP and other geometric problems'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 2-11.
  (MINIMUM K-SPANNING TREE, MINIMUM GEOMETRIC 3-DEGREE SPANNING TREE, MINIMUM GEOMETRIC STEINER TREE, MINIMUM GEOMETRIC TRAVELING SALESPERSON)

32
  Arora, S. (1997),
  ``Nearly linear time approximation schemes for Euclidean TSP and other geometric problems'',
  Proc. 38th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 554-563.
  (MINIMUM GEOMETRIC STEINER TREE, MINIMUM GEOMETRIC TRAVELING SALESPERSON)

33
  Arora, S., Babai, L., Stern, J., and Sweedyk, Z. (1997),
  ``The hardness of approximate optima in lattices, codes, and systems of linear equation'',
  J. Comput. System Sci. 54, 317-331.
  (MAXIMUM SATISFYING LINEAR SUBSYSTEM, MINIMUM UNSATISFYING LINEAR SUBSYSTEM, MAXIMUM HYPERPLANE CONSISTENCY, NEAREST LATTICE VECTOR, NEAREST CODEWORD)

34
  Arora, S., Frieze, A., and Kaplan, H. (1996),
  ``A new rounding procedure for the assignment problem with applications to dense graph arrangement problems'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 21-30.
  (MINIMUM FEEDBACK ARC SET, MINIMUM LINEAR ARRANGEMENT, MINIMUM CUT LINEAR ARRANGEMENT, MAXIMUM BETWEENNESS)

35
  Arora, S., Grigni, M., Karger, D., Klein, P., and Woloszyn, A. (1998),
  ``A polynomial-time approximation scheme for Weighted planar graph TSP'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 33-41.
  (MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

36
  Arora, S., and Karakostas, G. (1999),
  ``Approximation schemes for minimum latency problems'',
  Proc. 31st Ann. ACM Symp. on Theory of Comp., ACM, to appear.
  (MINIMUM TRAVELING REPAIRMAN)

37
  Arora, S., Karger, D., and Karpinski, M. (1995),
  ``Polynomial time approximation schemes for dense instances of NP-hard problems'',
  Proc. 27th Ann. ACM Symp. on Theory of Comp., ACM, 284-293.
  (MAXIMUM K-COLORABLE SUBGRAPH, MAXIMUM EDGE SUBGRAPH, MAXIMUM CUT, MAXIMUM DIRECTED CUT, MINIMUM K-CUT, MINIMUM MULTIWAY CUT, MINIMUM B-BALANCED CUT, MAXIMUM SET SPLITTING, MAXIMUM K-SATISFIABILITY)

38
  Asano, T., Hori, K., Ono, T., and Hirata, T. (1997),
  ``A theoretical framework of hybrid approaches to MAX SAT'',
  Proc. 8th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 1350, Springer-Verlag, 153-162.
  (MAXIMUM SATISFIABILITY)

39
  Assmann, S. F., Johnson, D. S., Kleitman, D. J., and Leung, J. Y. (1984),
  ``On a dual version of the one-dimensional bin packing problem'',
  J. Algorithms 5, 502-525.
  (MAXIMUM D-VECTOR COVERING)

40
  Aumann, Y., and Rabani, Y. (1995),
  ``Improved bounds for all optical routing'',
  Proc. 6th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 567-576.
  (MAXIMUM DISJOINT CONNECTING PATHS)

41
  Aumann, Y., and Rabani, Y. (1998),
  ``An approximate min-cut max-flow theorem and approximation algorithm'',
  SIAM J. Comp. 27, 291-301.
  (MINIMUM RATIO-CUT)

42
  Ausiello, G., Crescenzi, P., Gambosi, G., Kann, V., Marchetti Spaccamela, A., and Protasi, M. (1999),
  Complexity and Approximation. Combinatorial Optimization Problems and their Approximability Properties,
  Springer-Verlag, Berlin.
  (MAXIMUM K-SATISFIABILITY)

43
  Ausiello, G., D'Atri, A., and Protasi, M. (1980),
  ``Structure preserving reductions among convex optimization problems'',
  J. Comput. System Sci. 21, 136-153.
  (MINIMUM FEEDBACK VERTEX SET, MAXIMUM SET PACKING, MINIMUM SET COVER, MINIMUM HITTING SET)

44
  Ausiello, G., D'Atri, A., and Protasi, M. (1981),
  ``Lattice theoretic ordering properties for NP-complete optimization problems'',
  Annales Societatis Mathematicae Polonae 4, 83-94.
  (MAXIMUM DISTINGUISHED ONES)

45
  Averbakh, I., and Berman, O. (1997),
  ``(p-1)/(p+1)-approximate algorithms for p-traveling salesmen problems on a tree with minmax objective'',
  Disc. Appl. Math. 75, 201-216.
  (MINIMUM METRIC TRAVELING K-SALESPERSON PROBLEM)

46
  Awerbuch, B., and Azar, Y. (1997),
  ``Buy-at-bulk network design'',
  Proc. 38th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 542-547.
  (MINIMUM SINGLE-SINK EDGE INSTALLATION)

47
  Bafna, V., Berman, P., and Fujito, T. (1994),
  ``Approximating feedback vertex set for undirected graphs within ratio 2'',
  Unpublished manuscript.
  (MINIMUM FEEDBACK VERTEX SET)

48
  Bafna, V., Lawler, E. L., and Pevzner, P. A. (1997),
  ``Approximation algorithms for multiple sequence alignment'',
  Theoretical Comput. Sci. 182, 233-244.
  (MINIMUM TREE ALIGNMENT)

49
  Bafna, V., and Pevzner, P. A. (1995),
  ``Sorting permutations by transpositions'',
  Proc. 6th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 614-621.
  (MINIMUM SORTING BY REVERSALS)

50
  Baker, B. S. (1994),
  ``Approximation algorithms for NP-complete problems on planar graphs'',
  J. ACM 41, 153-180.
  (MINIMUM VERTEX COVER, MINIMUM DOMINATING SET, MINIMUM EDGE DOMINATING SET, MAXIMUM TRIANGLE PACKING, MAXIMUM H-MATCHING, MAXIMUM INDEPENDENT SET, MAXIMUM K-COLORABLE INDUCED SUBGRAPH)

51
  Bandelt, H., Crama, Y., and Spieksma, F. C. R. (1994),
  ``Approximation algorithms for multi-dimensional assignment problems with decomposable costs'',
  Disc. Appl. Math. 49, 25-50.
  (MINIMUM 3-DIMENSIONAL ASSIGNMENT)

52
  Bar-Ilan, J., Kortsarz, G., and Peleg, D. (1996),
  ``Generalized submodular cover problems and applications'',
  Proc. 4th Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 110-118.
  (MINIMUM STEINER TREE)

53
  Bar-Ilan, J., and Peleg, D. (1991),
  ``Approximation algorithms for selecting network centers'',
  Proc. 2nd Workshop on Algorithms and Data Structures, Lecture Notes in Comput. Sci. 519, Springer-Verlag, 343-354.
  (MINIMUM K-CENTER)

54
  Bar-Noy, A., Bellare, M., Halldórsson, M. M., Shachnai, H., and Tamir, T. (1998),
  ``On chromatic sums and distributed resource allocation'',
  Inform. and Comput. 140, 183-202.
  (MINIMUM COLOR SUM)

55
  Bar-Noy, A., and Kortsarz, G. (1998),
  ``The minimum color sum of bipartite graphs'',
  J. Algorithms 28, 339-365.
  (MINIMUM COLOR SUM)

56
  Bar-Yehuda, R., and Even, S. (1981),
  ``A linear-time approximation algorithm for the weighted vertex cover problem'',
  J. Algorithms 2, 198-203.
  (MINIMUM VERTEX COVER, MINIMUM SET COVER)

57
  Bar-Yehuda, R., and Even, S. (1985),
  ``A local-ratio theorem for approximating the weighted vertex cover problem'', in
  Analysis and Design of Algorithms for Combinatorial Problems,
  volume 25 of Annals of Disc. Math., , Annals of Disc. Math., Elsevier science publishing company, Amsterdam, 27-46.
  (MINIMUM VERTEX COVER)

58
  Bar-Yehuda, R., and Moran, S. (1984),
  ``On approximation problems related to the independent set and vertex cover problems'',
  Disc. Appl. Math. 9, 1-10.
  (MINIMUM DOMINATING SET)

59
  Bar-Yehuda, Reuven (1998),
  ``A linear time 2-approximation algorithm for the min clique-complement problem'',
  Technical Report CS0933, Technion CS Technical Reports.
  `http://www.cs.technion.ac.il/i-res.html`
  (MINIMUM EDGE DELETION TO OBTAIN SUBGRAPH WITH PROPERTY P)

60
  Bartal, Y., Leonardi, S., Marchetti-Spaccamela, A., Sgall, J., and Stougie, L. (1996),
  ``Multiprocessor scheduling with rejection'',
  Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 95-103.
  (MINIMUM MULTIPROCESSOR SCHEDULING)

61
  Barvinok, A. I. (1996),
  ``Two algorithmic results for the traveling salesman problem'',
  Math. Oper. Res. 21, 65-84.
  (MINIMUM GEOMETRIC TRAVELING SALESPERSON)

62
  Bellare, M. (1993),
  ``Interactive proofs and approximation: reductions from two provers in one round'',
  Proc. 2nd Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 266-274.
  (LONGEST PATH, MAXIMUM PRIORITY FLOW, MAXIMUM CAPACITY REPRESENTATIVES)

63
  Bellare, M., Goldreich, O., and Sudan, M. (1998),
  ``Free bits, PCPs and non-approximability - towards tight results'',
  SIAM J. Comp. 27, 804-915.
  (MINIMUM GRAPH COLORING, MAXIMUM CLIQUE, LONGEST COMMON SUBSEQUENCE, MAXIMUM COMPATIBLE BINARY CONSTRAINT SATISFACTION)

64
  Bellare, M., and Rogaway, P. (1995),
  ``The complexity of approximating a nonlinear program'',
  Math. Programming 69, 429-441.
  (MAXIMUM QUADRATIC PROGRAMMING)

65
  Bender, M. A., Chakrabarti, S., and Muthukrishnan, S. (1998),
  ``Flow and stretch metrics for scheduling continuous job streams'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 270-279.
  (MINIMUM SEQUENCING WITH RELEASE TIMES)

66
  Berger, B., and Cowen, L. (1991),
  ``Complexity results and algorithms for -constrained scheduling'',
  Proc. Second Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 137-147.
  (MINIMUM PRECEDENCE CONSTRAINED SCHEDULING)

67
  Berger, B., and Shor, P. W. (1990),
  ``Approximation algorithms for the maximum acyclic subgraph problem'',
  Proc. First Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 236-243.
  (MINIMUM FEEDBACK ARC SET)

68
  Berman, F., Johnson, D., Leighton, T., Shor, P. W., and Snyder, L. (1990),
  ``Generalized planar matching'',
  J. Algorithms 11, 153-184.
  (MAXIMUM H-MATCHING)

69
  Berman, P., and Fujito, T. (1995),
  ``Approximating independent sets in degree 3 graphs'',
  Proc. 4th Workshop on Algorithms and Data Structures, Lecture Notes in Comput. Sci. 955, Springer-Verlag, 449-460.
  (MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, MAXIMUM SET PACKING)

70
  Berman, P., and Karpinski, M. (1998),
  ``On some tighter inapproximability results'',
  Technical Report TR98-029, ECCC.
  `ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1998/TR98-029/index.html`
  (MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, MAXIMUM SATISFYING LINEAR SUBSYSTEM, MAXIMUM K-SATISFIABILITY, MINIMUM SORTING BY REVERSALS)

71
  Berman, P., and Schnitger, G. (1992),
  ``On the complexity of approximating the independent set problem'',
  Inform. and Comput. 96, 77-94.
  (MAXIMUM INDUCED CONNECTED SUBGRAPH WITH PROPERTY P, LONGEST PATH WITH FORBIDDEN PAIRS, LONGEST COMMON SUBSEQUENCE, MAXIMUM BOUNDED 0-1 PROGRAMMING, MAXIMUM K-CONSTRAINT SATISFACTION, LONGEST COMPUTATION)

72
  Bern, M., and Plassmann, P. (1989),
  ``The Steiner problem with edge lengths 1 and 2'',
  Inform. Process. Lett. 32, 171-176.
  (MINIMUM STEINER TREE)

73
  Bernstein, D., Rodeh, M., and Gertner, I. (1989),
  ``Approximation algorithms for scheduling arithmetic expressions on pipelined machines'',
  J. Algorithms 10, 120-139.
  (MINIMUM PRECEDENCE CONSTRAINED SEQUENCING WITH DELAYS)

74
  Bertsimas, D., Teo, C-P., and Vohra, R. (1996),
  ``On dependent randomized rounding algorithms'',
  Proc. 5th Int. Conf. on Integer Prog. and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1084, Springer-Verlag, 330-344.
  (MINIMUM EDGE COLORING, MAXIMUM SATISFIABILITY, MINIMUM K-SATISFIABILITY)

75
  Blache, G., Karpinski, M., and Wirtgen, J. (1998),
  ``On approximation intractability of the bandwidth problem'',
  Technical Report TR98-014, ECCC.
  `ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1998/TR98-014/index.html`
  (MINIMUM BANDWIDTH)

76
  Blaha, K. D. (1992),
  ``Minimum bases for permutation groups: the greedy approximation'',
  J. Algorithms 13, 297-306.
  (MINIMUM PERMUTATION GROUP BASE)

77
  Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, B., Raghavan, P., and Sudan, M. (1994),
  ``The minimum latency problem'',
  Proc. 26th Ann. ACM Symp. on Theory of Comp., ACM, 163-171.
  (MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

78
  Blum, A., Jiang, T., Li, M., Tromp, J., and Yannakakis, M. (1994),
  ``Linear approximation of shortest superstrings'',
  J. ACM 41, 630-647.
  (SHORTEST COMMON SUPERSTRING)

79
  Blum, A., Ravi, R., and Vempala, S. (1996),
  ``A constant-factor approximation algorithm for the k-MST problem'',
  Proc. 28th Ann. ACM Symp. on Theory of Comp., ACM, 442-448.
  (MINIMUM STEINER TREE)

80
  Blum, Avrim, and Karger, David (1997),
  ``An -coloring algorithm for 3-colorable graphs'',
  Inform. Process. Lett. 61, 49-53.
  (MINIMUM GRAPH COLORING)

81
  Bodlaender, H. L., Gilbert, J. R., Hafsteinsson, H., and Kloks, T. (1995),
  ``Approximating treewidth, pathwidth, frontsize and shortest elimination tree'',
  J. Algorithms 18, 238-255.
  (MINIMUM TREE WIDTH)

82
  Bonizzoni, P., Duella, M., and Mauri, G. (1994),
  ``Approximation complexity of longest common subsequence and shortest common supersequence over fixed alphabet'',
  Technical Report 117/94, Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano.
  (SHORTEST COMMON SUPERSEQUENCE, LONGEST COMMON SUBSEQUENCE)

83
  Boppana, R., and Halldórsson, M. M. (1992),
  ``Approximating maximum independent sets by excluding subgraphs'',
  Bit 32, 180-196.
  (MAXIMUM CLIQUE)

84
  Bshouty, N., and Burroughs, L. (1998),
  ``Massaging a linear programming solution to give a 2-approximation for a generalization of the vertex cover problem'',
  Proc. 15th Ann. Symp. on Theoretical Aspects of Comput. Sci., , Lecture Notes in Comput. Sci., Springer-Verlag, 298-308.
  (MINIMUM VERTEX COVER)

85
  Bui, T. N., and Jones, C. (1992),
  ``Finding good approximate vertex and edge partitions is NP-hard'',
  Inform. Process. Lett. 42, 153-159.
  (MINIMUM B-BALANCED CUT, MINIMUM B-VERTEX SEPARATOR)

86
  Calinescu, G., Fernandes, C. G., Finkler, U., and Karloff, H. (1996),
  ``A better approximation algorithm for finding planar subgraphs'',
  Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 16-25.
  (MAXIMUM PLANAR SUBGRAPH)

87
  Calinescu, G., Karloff, H., and Rabani, Y. (1998),
  ``An improved approximation algorithm for multiway cut'',
  Proc. 30th Ann. ACM Symp. on Theory of Comp., ACM-SIAM, 48-52.
  (MINIMUM MULTIWAY CUT)

88
  Chakrabati, S., Phillips, C. A., Schulz, A. S., Shmoys, D. B., Stein, C., and Wein, J. (1996),
  ``Improved scheduling algorithms for minsum criteria'',
  Proc. 23rd Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1099, Springer-Verlag, 646-657.
  (MINIMUM WEIGHTED COMPLETION TIME SCHEDULING)

89
  Chandra, A. K., Hirschberg, D. S., and Wong, C. K. (1976),
  ``Approximate algorithms for some generalized knapsack problems'',
  Theoretical Comput. Sci. 3, 293-304.
  (MAXIMUM INTEGER M-DIMENSIONAL KNAPSACK, MAXIMUM INTEGER K-CHOICE KNAPSACK)

90
  Chandra, B., and Halldórsson, M. M. (1999),
  ``Greedy local improvement and weighted set packing approximation'',
  Proc. 10th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 169-176.
  (MAXIMUM H-MATCHING, MAXIMUM SET PACKING)

91
  Charikar, M., Chekuri, C., Cheung, T., Dai, Z., Goel, A., Guha, S., and Li, M. (1998),
  ``Approximation algorithms for directed Steiner problems'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 192-200.
  (MINIMUM STEINER TREE, MINIMUM GENERALIZED STEINER NETWORK)

92
  Chaudhary, A., and Vishwanathan, S. (1997),
  ``Approximation algorithms for the achromatic number'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 558-563.
  (MAXIMUM ACHROMATIC NUMBER)

93
  Chekuri, C., Motwani, R., Natarajan, B., and Stein, C. (1997),
  ``Approximation techniques for average completion time scheduling'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 609-618.
  (MINIMUM SEQUENCING WITH RELEASE TIMES)

94
  Chen, B. (1993),
  ``A better heuristic for preemptive parallel machine scheduling with batch setup times'',
  SIAM J. Comp. 22, 1303-1318.
  (MINIMUM PREEMPTIVE SCHEDULING WITH SET-UP TIMES)

95
  Chen, B. (1994),
  ``Scheduling multiprocessor flow shops'', in
  Advances in Optimization and Approximation, Kluwer Academic Publishers, The Netherlands, 1-8.
  (MINIMUM FLOW-SHOP SCHEDULING)

96
  Chen, B., Glass, C. A., Potts, C. N., and Strusevich, V. A. (1996),
  ``A new heuristic for three-machine flow shop scheduling'',
  Oper. Res. 44, 891-898.
  (MINIMUM FLOW-SHOP SCHEDULING)

97
  Chen, B., Potts, C. N., and Strusevich, V. A. (1995),
  ``Approximation algorithms for two-machine flow shop scheduling with batch setup times'',
  Math. Programming , to appear.
  (MINIMUM TWO-PROCESSOR FLOW-SHOP SCHEDULING WITH BATCH SET-UP TIMES)

98
  Chen, B., and Strusevich, V. A. (1993a),
  ``Approximation algorithms for three-machine open shop scheduling'',
  ORSA J. Comput. 5, 321-326.
  (MINIMUM OPEN-SHOP SCHEDULING)

99
  Chen, B., and Strusevich, V. A. (1993b),
  ``Worst-case analysis of heuristics for open shops with parallel machines'',
  European J. Oper. Res. 70, 379-390.
  (MINIMUM OPEN-SHOP SCHEDULING)

100
  Chen, Z.-Z. (1996),
  ``Practical approximation schemes for maximum induced-subgraph problems on K3,3-free or K5-free graphs'',
  Proc. 23rd Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1099, Springer-Verlag, 268-279.
  (MAXIMUM INDUCED SUBGRAPH WITH PROPERTY P)

101
  Cheriyan, J., and Thurimella, R. (1996),
  ``Approximating minimum-size k-connected spanning subgraphs via matching'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 292-301.
  (MINIMUM K-VERTEX CONNECTED SUBGRAPH, MINIMUM K-EDGE CONNECTED SUBGRAPH)

102
  Chlebikova, J. (1996),
  ``Approximability of the Maximally balanced connected partition problem in graphs'',
  Inform. Process. Lett. 60, 225-230.
  (MAXIMUM BALANCED CONNECTED PARTITION, MAXIMUM LEAF SPANNING TREE)

103
  Choi, J., Sellen, J., and Yap, C. K. (1997),
  ``Approximate Euclidean shortest paths in 3-space'',
  International J. Comput. Geom. Appl. 7, 271-295.
  (SHORTEST PATH MOTION IN 3 DIMENSIONS)

104
  Chor, B., and Sudan, M. (1998),
  ``A geometric approach to betweenness'',
  SIAM J. Disc. Math. 11, 511-523.
  (MAXIMUM BETWEENNESS)

105
  Christie, D. A. (1998),
  ``A 3/2-approximation algorithm for Sorting by reversals'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 244-252.
  (MINIMUM SORTING BY REVERSALS)

106
  Christofides, N. (1976),
  ``Worst-case analysis of a new heuristic for the travelling salesman problem'',
  Technical Report 388, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh.
  (MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

107
  Chudak, F. A., and Shmoys, D. B. (1997),
  ``Approximation algorithms for precedence-constrained scheduling problems on parallel machines that run at different speed'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 581-590.
  (MINIMUM PRECEDENCE CONSTRAINED SCHEDULING)

108
  Chvátal, V. (1979),
  ``A greedy heuristic for the set covering problem'',
  Math. Oper. Res. 4, 233-235.
  (MINIMUM SET COVER)

109
  Clementi, A., and Ianni, M. Di (1996),
  ``On the hardness of approximating optimum schedule problems in store and forward networks'',
  IEEE/ACM Transaction on Networking 4, 272-280.
  (MINIMUM SCHEDULE LENGTH)

110
  Clementi, A., and Trevisan, L. (1996),
  ``Improved non-approximability results for vertex cover problems with density constraints'',
  Proc. 2nd Ann. Int. Conf. on Computing and Combinatorics, Lecture Notes in Comput. Sci. 1090, Springer-Verlag, 333-342.
  (MINIMUM VERTEX COVER)

111
  Cody, R. A., and Coffman, E. G., Jr (1976),
  ``Record allocation for minimizing expected retrieval costs on drum-like storage devices'',
  J. ACM 23, 103-115.
  (MINIMUM SUM OF SQUARES)

112
  Coffman, E. G., Jr, Garey, M. R., and Johnson, D. S. (1997),
  ``Approximation algorithms for bin-packing - a survey'', in
  Approximation Algorithms for NP-hard Problems, PWS Publishing Company, Boston, 46-93.
  (MINIMUM BIN PACKING)

113
  Coffman, E. G., Jr, Garey, M. R., Johnson, D. S., and Lapaugh, A. S. (1985),
  ``Scheduling file transfers'',
  SIAM J. Comp. 14, 744-780.
  (MINIMUM FILE TRANSFER SCHEDULING)

114
  Cornuejols, G., Fisher, M., and Nemhauser, G. (1977),
  ``Location of bank accounts to optimize float: An analytic study of exact and approximate algorithms'',
  Management Sci. 23, 789-810.
  (MAXIMUM K-FACILITY LOCATION)

115
  Cowen, L. J., Goddard, W., and Jesurum, C. E. (1997),
  ``Coloring with defect'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 548-557.
  (MINIMUM GRAPH COLORING)

116
  Crama, Y., and Spieksma, F. C. R. (1992),
  ``Approximation algorithms for three-dimensional assignment problems with triangle inequalities'',
  European J. Oper. Res. 60, 273-279.
  (MINIMUM 3-DIMENSIONAL ASSIGNMENT)

117
  Crescenzi, P., Kann, V., Silvestri, R., and Trevisan, L. (1995),
  ``Structure in approximation classes'',
  Proc. 1st Ann. Int. Conf. on Computing and Combinatorics, Lecture Notes in Comput. Sci. 959, Springer-Verlag, 539-548.
  (MINIMUM EDGE COLORING, MINIMUM DEGREE SPANNING TREE, MINIMUM BIN PACKING)

118
  Crescenzi, P., and Panconesi, A. (1991),
  ``Completeness in approximation classes'',
  Inform. and Comput. 93, 241-262.
  (MAXIMUM WEIGHTED SATISFIABILITY WITH BOUND)

119
  Crescenzi, P., Silvestri, R., and Trevisan, L. (1994),
  ``On the query complexity of complete problems in approximation classes'',
  Unpublished manuscript.

120
  Crescenzi, P., Silvestri, R., and Trevisan, L. (1996),
  ``To weight or not to weight: Where is the question?'',
  Proc. 4th Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 68-77.
  (MAXIMUM CUT, MAXIMUM DIRECTED CUT, MAXIMUM SATISFIABILITY, MAXIMUM K-SATISFIABILITY)

121
  Crescenzi, P., and Trevisan, L. (1994),
  ``On approximation scheme preserving reducibility and its applications'',
  Proc. 14th Ann. Conf. on Foundations of Software Tech. and Theoret. Comput. Sci., Lecture Notes in Comput. Sci. 880, Springer-Verlag, 330-341.

122
  Dahlhaus, E., Johnson, D. S., Papadimitriou, C. H., Seymour, P. D., and Yannakakis, M. (1994),
  ``The complexity of multiterminal cuts'',
  SIAM J. Comp. 23, 864-894.
  (MINIMUM MULTIWAY CUT)

123
  d'Anzeo, C. (1996),
  ``Optimization complexity of the SCS problem given a longest common subsequence'',
  Unpublished manuscript.
  (SHORTEST COMMON SUPERSEQUENCE)

124
  DasGupta, B., He, X., Jiang, T., Li, M., Tromp, J., and Zhang, L. (1997),
  ``On distances between phylogenetic trees'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 427-436.
  (MINIMUM PHYLOGENETIC TREE DISTANCE)

125
  Datta, A. K., and Sen, R. K. (1995),
  ``1-approximation algorithm for bottleneck disjoint path matching'',
  Inform. Process. Lett. 55, 41-44.
  (MINIMUM BOTTLENECK PATH MATCHING)

126
  Di Ianni, M. (1998),
  ``Efficient delay routing'',
  Theoretical Comput. Sci. 196, 131-151.
  (MINIMUM SCHEDULE LENGTH)

127
  Doddi, S., Marathe, M. V., Mirzaian, A., Moret, B. M. E., and Zhu, B. (1997),
  ``Map labeling and its generalizations'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 148-157.
  (MAXIMUM MAP LABELING)

128
  Drangmeister, K. U., Krumke, S. O., Marathe, M. V., Noltemeier, H., and Ravi, S. S. (1998),
  ``Modifying edges of a network to obtain short subgraphs'',
  Theoretical Comput. Sci. 203, 91-121.
  (MINIMUM STEINER TREE)

129
  Dudek, G., Romanik, K., and Whitesides, S. (1994),
  ``Localizing a robot with minimum travel'',
  Technical Report SOCS-94.5, McGill University.
  (MINIMUM TRAVEL ROBOT LOCALIZATION)

130
  Duh, R., and Fürer, M. (1997),
  ``Approximation of k-set cover by semi-local optimization'',
  Proc. 29th Ann. ACM Symp. on Theory of Comp., ACM, 256-265.
  (MINIMUM GRAPH COLORING, MINIMUM CLIQUE PARTITION, MINIMUM CLIQUE COVER, MINIMUM SET COVER)

131
  Eades, P., and Wormald, N. C. (1994),
  ``Edge crossings in drawings of bipartite graphs'',
  Algorithmica 11, 379-403.
  (MINIMUM CROSSING NUMBER)

132
  Engebretsen, L. (1999),
  ``An explicit lower bound for TSP with distances one and two'',
  Proc. 16th Ann. Symp. on Theoretical Aspects of Comput. Sci., Lecture Notes in Comput. Sci. 1563, Springer-Verlag, 373-382.
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  (MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

133
  Eppstein, D. (1992),
  ``Approximating the minimum weight triangulation'',
  Proc. Third Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 48-57.
  (MINIMUM LENGTH TRIANGULATION)

134
  Errico, B., and Rosati, R. (1995),
  ``Minimal models in propositional logics: approximation results'',
  Proc. of 5th Italian Conference on Theoretical Computer Science, Word Scientific, 547-562.
  (MINIMUM DISTINGUISHED ONES)

135
  Even, G., Naor, J., Rao, S., and Schieber, B. (1995),
  ``Divide-and-conquer approximation algorithms via spreading metrics'',
  Proc. 36th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 62-71.
  (MINIMUM CUT LINEAR ARRANGEMENT)

136
  Even, G., Naor, J., Rao, S., and Schieber, B. (1997),
  ``Fast approximate graph partitioning algorithms'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 639-648.
  (MINIMUM B-BALANCED CUT)

137
  Even, G., Naor, J., Schieber, B., and Sudan, M. (1995),
  ``Approximating minimum feedback sets and multi-cuts in directed graphs'',
  Proc. 4th Int. Conf. on Integer Prog. and Combinatorial Optimization, Lecture Notes in Comput. Sci. 920, Springer-Verlag, 14-28.
  (MINIMUM FEEDBACK VERTEX SET, MINIMUM FEEDBACK ARC SET)

138
  Even, G., Naor, J., and Zosin, L. (1996),
  ``An 8-approximation algorithm for the subset feedback vertex set problem'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 310-319.
  (MINIMUM FEEDBACK VERTEX SET)

139
  Farach, M., Kannan, S., and Warnow, T. (1993),
  ``A robust model for finding optimal evolutionary trees'',
  Proc. 25th Ann. ACM Symp. on Theory of Comp., ACM, 137-145.
  (MINIMUM SIZE ULTRAMETRIC TREE)

140
  Farach, M., and Liberatore, V. (1998),
  ``On local register allocation'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 564-573.
  (MINIMUM LOCAL REGISTER ALLOCATION)

141
  Feder, T., and Greene, D. H. (1988),
  ``Optimal algorithms for approximate clustering'',
  Proc. 20th Ann. ACM Symp. on Theory of Comp., ACM, 434-444.
  (MINIMUM METRIC BOTTLENECK WANDERING SALESPERSON PROBLEM, MINIMUM K-CENTER, MINIMUM K-CLUSTERING)

142
  Feige, U. (1996),
  ``A threshold of for approximating set cover'',
  Proc. 28th Ann. ACM Symp. on Theory of Comp., ACM, 314-318.
  (MINIMUM DOMINATING SET, MINIMUM SET COVER)

143
  Feige, U., and Goemans, M. X. (1995),
  ``Approximating the value of two prover proof systems, with applications to MAX 2SAT and MAX DICUT'',
  Proc. 3rd Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 182-189.
  (MAXIMUM DIRECTED CUT, MAXIMUM K-SATISFIABILITY)

144
  Feige, U., and Kilian, J. (1996),
  ``Zero knowledge and the chromatic number'',
  Proc. Eleventh Ann. IEEE Conf. on Comp. Complexity, IEEE Computer Society, 278-287.
  (MINIMUM GRAPH COLORING, MINIMUM COLOR SUM)

145
  Feige, U., Kortsarz, G., and Peleg, D. (1995),
  ``The dense k-subgraph problem'',
  Unpublished manuscript.
  (MAXIMUM EDGE SUBGRAPH)

146
  Fekete, S., Khuller, S., Klemmstein, M., Raghavachari, B., and Young, N. (1996),
  ``A network-flow technique for finding low-weight bounded-degree spanning trees'',
  Proc. 5th Int. Conf. on Integer Prog. and Combinatorial Optimization, Lecture Notes in Comput. Sci. 1084, Springer-Verlag, 105-117.
  (MINIMUM GEOMETRIC 3-DEGREE SPANNING TREE)

147
  Feo, T., Goldschmidt, O., and Khellaf, M. (1992),
  ``One half approximation algorithms for the k-partition problem'',
  Oper. Res. 40, 170-172.
  (MINIMUM K-CLUSTERING SUM)

148
  Feo, T., and Khellaf, M. (1990),
  ``A class of bounded approximation algorithms for graph partitioning'',
  Networks 20, 181-195.
  (MINIMUM K-CLUSTERING SUM)

149
  Fernandes, C. G. (1997),
  ``A better approximation ratio for the minimum k-edge-connected spanning subgraph problem'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 629-638.
  (MINIMUM K-EDGE CONNECTED SUBGRAPH)

150
  Fernandez de la Vega, W., and Karpinski, M. (1998),
  ``Polynomial time approximation of dense weighted instances of MAX-CUT'',
  Technical Report TR98-064, ECCC.
  `ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/1998/TR98-064/index.html`
  (MAXIMUM CUT)

151
  Fernandez de la Vega, W., and Kenyon, C. (1998),
  ``A randomized approximation scheme for metric MAX-CUT'',
  Proc. 39th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 468-471.
  (MAXIMUM CUT)

152
  Fernandez de la Vega, W., and Zissimopoulos, V. (1991),
  ``An approximation scheme for strip-packing of rectangles with bounded dimensions'',
  Technical Report 713, Laboratoire de Recherche en Informatique, Université de Paris, Orsay.
  (MINIMUM HEIGHT TWO DIMENSIONAL PACKING)

153
  Fialko, S., and Mutzel, P. (1998),
  ``A new approximation algorithm for the Planar augmentation problem'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 260-269.
  (MINIMUM BICONNECTIVITY AUGMENTATION)

154
  Floréen, P., and Orponen, P. (1993),
  ``Attraction radii in binary Hopfield nets are hard to compute'',
  Neural Comput. 5, 812-821.
  (MINIMUM ATTRACTION RADIUS FOR BINARY HOPFIELD NET)

155
  Formann, M., and Wagner, F. (1991),
  ``A packing problem with applications to lettering of maps'',
  Proc. 7th Ann. ACM Symp. Comput. Geom., ACM, 281-288.
  (MAXIMUM MAP LABELING)

156
  Fraser, C. B., and Irving, R. W. (1995),
  ``Approximation algorithms for the shortest common supersequence'',
  Nordic J. Comp. 2, 303-325.
  (SHORTEST COMMON SUPERSEQUENCE)

157
  Fraser, C. B., Irving, R. W., and Middendorf, M. (1996),
  ``Maximal common subsequences and minimal common supersequences'',
  Inform. and Comput. 124, 145-153.
  (LONGEST COMMON SUBSEQUENCE)

158
  Frederickson, G. N. (1979),
  ``Approximation algorithms for some postman problems'',
  J. ACM 26, 538-554.
  (MINIMUM CHINESE POSTMAN FOR MIXED GRAPHS)

159
  Frederickson, G. N., Hecht, M. S., and Kim, C. E. (1978),
  ``Approximation algorithms for some routing problems'',
  SIAM J. Comp. 7, 178-193.
  (MINIMUM METRIC TRAVELING K-SALESPERSON PROBLEM, MINIMUM K-CHINESE POSTMAN PROBLEM, MINIMUM STACKER CRANE PROBLEM, MINIMUM K-STACKER CRANE PROBLEM)

160
  Frederickson, G. N., and Jájá, J. (1981),
  ``Approximation algorithms for several graph augmentation problems'',
  SIAM J. Comp. 10, 270-283.
  (MINIMUM BICONNECTIVITY AUGMENTATION, MINIMUM STRONG CONNECTIVITY AUGMENTATION)

161
  Frederickson, G. N., and Jájá, J. (1982),
  ``On the relationship between the biconnectivity augmentation and traveling salesman problems'',
  Theoretical Comput. Sci. 19, 189-201.
  (MINIMUM K-VERTEX CONNECTED SUBGRAPH, MINIMUM BICONNECTIVITY AUGMENTATION)

162
  Frederickson, G. N., and Solis-Oba, R. (1996),
  ``Increasing the weight of minimum spanning trees'',
  Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 539-546.
  (MAXIMUM MINIMUM SPANNING TREE DELETING K EDGES)

163
  Frieze, A., Galbiati, G., and Maffioli, F. (1982),
  ``On the worst-case performance of some algorithms for the asymmetric traveling salesman problem'',
  Networks 12, 23-39.
  (MINIMUM METRIC TRAVELING SALESPERSON PROBLEM)

164
  Frieze, A., and Jerrum, M. (1997),
  ``Improved approximation algorithms for MAX k-CUT and MAX BISECTION'',
  Algorithmica 18, 67-81.
  (MAXIMUM K-COLORABLE SUBGRAPH, MAXIMUM CUT, MAXIMUM K-CUT)

165
  Fujito, T. (1996),
  ``A unified local ratio approximation of node-deletion problems'',
  Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 167-178.
  (MINIMUM VERTEX DELETION TO OBTAIN SUBGRAPH WITH PROPERTY P)

166
  Fürer, M., and Raghavachari, B. (1994),
  ``Approximating the minimum-degree Steiner tree to within one of optimal'',
  J. Algorithms 17, 409-423.
  (MINIMUM DEGREE SPANNING TREE)

167
  Galbiati, G., Maffioli, F., and Morzenti, A. (1994),
  ``A short note on the approximability of the maximum leaves spanning tree problem'',
  Inform. Process. Lett. 52, 45-49.
  (MAXIMUM LEAF SPANNING TREE)

168
  Galbiati, G., Maffioli, F., and Morzenti, A. (1995),
  ``On the approximability of some maximum spanning tree problems'',
  Proc. 2nd Int. Symp. Latin American Theoretical Informatics, Lecture Notes in Comput. Sci. 911, Springer-Verlag, 300-311.
  (MAXIMUM LEAF SPANNING TREE)

169
  Garey, M. R., and Graham, R. L. (1975),
  ``Bounds for multiprocessor scheduling with resource constraints'',
  SIAM J. Comp. 4, 187-200.
  (MINIMUM RESOURCE CONSTRAINED SCHEDULING)

170
  Garey, M. R., and Johnson, D. S. (1979),
  Computers and Intractability: A guide to the theory of NP-completeness,
  W. H. Freeman and Company, San Francisco.
  (MINIMUM DEGREE SPANNING TREE, MINIMUM BIN PACKING)

171
  Garg, A., and Tamassia, R. (1994),
  ``On the computational complexity of upward and rectilinear planarity testing'',
  Proc. DIMACS Int. Workshop on Graph Drawing, Lecture Notes in Comput. Sci. 894, Springer-Verlag, 286-297.
  (MINIMUM BEND NUMBER)

172
  Garg, N. (1996),
  ``A 3-approximation for the minimum tree spanning k vertices'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 302-309.
  (MINIMUM K-SPANNING TREE, MINIMUM TRAVELING REPAIRMAN)

173
  Garg, N., Konjevod, G., and Ravi, R. (1998),
  ``A polylogarithmic approximation algorithm for the group Steiner tree problem'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 253-259.
  (MINIMUM STEINER TREE)

174
  Garg, N., Santosh, V. S., and Singla, A. (1993),
  ``Improved approximation algorithms for biconnected subgraphs via better lower bounding techniques'',
  Proc. 4th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 103-111.
  (MINIMUM K-VERTEX CONNECTED SUBGRAPH)

175
  Garg, N., Saran, H., and Vazirani, V. (1994),
  ``Finding separator cuts in planar graphs within twice the optimal'',
  Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 14-23.
  (MINIMUM B-BALANCED CUT)

176
  Garg, N., Vazirani, V. V., and Yannakakis, M. (1994),
  ``Multiway cuts in directed and node weighted graphs'',
  Proc. 21st Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 820, Springer-Verlag, 487-498.
  (MINIMUM VERTEX DELETION TO OBTAIN SUBGRAPH WITH PROPERTY P, MINIMUM VERTEX K-CUT, MINIMUM MULTIWAY CUT, MINIMUM MULTI-CUT)

177
  Garg, N., Vazirani, V. V., and Yannakakis, M. (1996),
  ``Approximate max-flow min-(multi)cut theorems and their applications'',
  SIAM J. Comp. 25, 235-251.
  (MINIMUM EDGE DELETION K-PARTITION, MINIMUM MULTI-CUT, MINIMUM EQUIVALENCE DELETION)

178
  Garg, N., Vazirani, V. V., and Yannakakis, M. (1997),
  ``Primal-dual approximation algorithms for integral flow and multicut in trees'',
  Algorithmica 18, 3-20.
  (MINIMUM MULTI-CUT, MAXIMUM INTEGRAL K-MULTICOMMODITY FLOW ON TREES, MINIMUM SET COVER)

179
  Gens, G. V., and Levner, E. V. (1979),
  ``Computational complexity of approximation algorithms for combinatorial problems'',
  Proc. 8th International Symp. on Mathematical Foundations of Comput. Sci., Lecture Notes in Comput. Sci. 74, Springer-Verlag, 292-300.
  (MAXIMUM KNAPSACK, MAXIMUM INTEGER K-CHOICE KNAPSACK)

180
  Gergov, J. (1996),
  ``Approximation algorithms for dynamic storage allocation'',
  Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 52-61.
  (MINIMUM DYNAMIC STORAGE ALLOCATION)

181
  Gil, J., and Itai, A. (1995),
  ``Packing trees'',
  Proc. 3rd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 979, Springer-Verlag, 113-127.
  (MINIMUM TREE COMPACT PACKING)

182
  Goemans, M. X., Goldberg, A. V., Plotkin, S., Shmoys, D. B., Tardos, É., and Williamson, D. P. (1994),
  ``Improved approximation algorithms for network design problems'',
  Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 223-232.
  (MINIMUM GENERALIZED STEINER NETWORK)

183
  Goemans, M. X., and Kleinberg, J. M. (1996),
  ``An improved approximation ratio for the minimum latency problem'',
  Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 152-158.
  (MINIMUM TRAVELING REPAIRMAN)

184
  Goemans, M. X., Queyranne, M., Schulz, A. S., Skutella, M., and Wang, Y. (1998),
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185
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186
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187
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188
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189
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190
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191
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192
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193
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194
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195
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196
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197
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198
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199
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200
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201
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202
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203
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204
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205
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206
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207
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208
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209
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210
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211
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212
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213
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214
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215
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216
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217
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218
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219
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220
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221
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222
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223
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224
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225
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226
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227
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228
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229
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230
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231
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232
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233
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234
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235
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236
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237
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238
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239
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240
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241
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242
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243
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244
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245
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246
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247
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248
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249
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250
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251
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252
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253
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254
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255
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256
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257
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258
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259
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260
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261
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262
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263
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264
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265
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266
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267
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268
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269
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270
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271
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272
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273
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274
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275
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276
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277
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278
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279
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280
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281
  Karpinski, M., Wirtgen, J., and Zelikovsky, A. (1997),
  ``An approximation algorithm for the bandwidth problem on dense graphs'',
  Technical Report TR97-017, ECCC.
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282
  Karpinski, M., and Zelikovsky, A. (1997),
  ``Approximating dense cases of covering problems'',
  Technical Report TR97-004, ECCC.
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283
  Karuno, Y., Nagamochi, H., and Ibaraki, T. (1993),
  ``Vehicle scheduling on a tree with release and handling times'',
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284
  Kavvadias, D., Papadimitriou, C. H., and Sideri, M. (1993),
  ``On Horn envelopes and hypergraph transversals'',
  Proc. 4th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 762, Springer-Verlag, 399-405.
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285
  Kellerer, H., Tautenhahn, T., and Woeginger, G. J. (1996),
  ``Approximability and nonapproximability results for minimizing total flow time on a single machine'',
  Proc. 28th Ann. ACM Symp. on Theory of Comp., ACM, 418-426.
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286
  Kenyon, C., and Rémila, E. (1996),
  ``Approximate strip packing'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 31-36.
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287
  Khanna, S. (1997),
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  Bell Labs Technical J. Spring, 36-41.
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288
  Khanna, S., Linial, N., and Safra, S. (1993),
  ``On the hardness of approximating the chromatic number'',
  Proc. 2nd Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 250-260.
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289
  Khanna, S., and Motwani, R. (1996),
  ``Toward a syntactic characterization of PTAS'',
  Proc. 28th Ann. ACM Symp. on Theory of Comp., ACM, 329-337.
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290
  Khanna, S., Motwani, R., Sudan, M., and Vazirani, U. (1999),
  ``On syntactic versus computational views of approximability'',
  SIAM J. Comp. 28, 164-191.
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291
  Khanna, S., Muthukrishnan, S., and Paterson, M. (1998),
  ``On approximating rectangle tiling and packing'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 384-393.
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292
  Khanna, S., Muthukrishnan, S., and Skiena, S. (1997),
  ``Efficient array partitioning'',
  Proc. 24th Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1256, Springer-Verlag, 616-626.
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293
  Khuller, S. (1997),
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294
  Khuller, S., Pless, R., and Sussmann, Y. J. (1997),
  ``Fault tolerant k-center problems'',
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295
  Khuller, S., and Raghavachari, B. (1996),
  ``Improved approximation algorithms for uniform connectivity problems'',
  J. Algorithms 21, 434-450.
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296
  Khuller, S., Raghavachari, B., and Rosenfeld, A. (1994),
  ``Localization in graphs'',
  Technical Report UMIACS-TR-94-92, University of Maryland, UMIACS.
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297
  Khuller, S., Raghavachari, B., and Young, N. (1993),
  ``Maintaining directed reachability with few edges'',
  Technical Report UMIACS-TR-93-87, University of Maryland, UMIACS.
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298
  Khuller, S., Raghavachari, B., and Young, N. (1995),
  ``Approximating the minimum equivalent digraph'',
  SIAM J. Comp. 24, 859-872.
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299
  Khuller, S., Raghavachari, B., and Young, N. (1996a),
  ``Low degree spanning trees of small weight'',
  SIAM J. Comp. 25, 355-368.
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300
  Khuller, S., Raghavachari, B., and Young, N. (1996b),
  ``On strongly connected digraphs with bounded cycle length'',
  Disc. Appl. Math. 69, 281-289.
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301
  Khuller, S., and Sussmann, Y. J. (1996),
  ``The capacitated k-center problem'',
  Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 152-166.
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302
  Khuller, S., and Thurimella, R. (1993),
  ``Approximation algorithms for graph augmentation'',
  J. Algorithms 14, 214-225.
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303
  Khuller, S., and Vishkin, U. (1994),
  ``Biconnectivity approximations and graph carvings'',
  J. ACM 41, 214-235.
  (MINIMUM GENERALIZED STEINER NETWORK, MINIMUM K-EDGE CONNECTED SUBGRAPH)

304
  Kim, S., and McNaughton, R. (1993),
  ``Computing the order of a locally testable automaton'',
  Unpublished manuscript.
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305
  Klein, P., Agrawal, A., Ravi, R., and Rao, S. (1990),
  ``Approximation through multicommodity flow'',
  Proc. 31st Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 726-737.
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306
  Klein, P., Plotkin, S. A., and Rao, S. (1993),
  ``Excluded minors, network decomposition, and multicommodity flow'',
  Proc. 25th Ann. ACM Symp. on Theory of Comp., ACM, 682-690.
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307
  Kleinberg, J., and Tardos, É. (1995),
  ``Approximations for the disjoint paths problem in high-diameter planar networks'',
  Proc. 27th Ann. ACM Symp. on Theory of Comp., ACM, 26-35.
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308
  Kleinberg, J. M. (1996),
  ``Single-source unsplittable flow'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 68-77.
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309
  Kloks, T., Kratsch, D., and Müller, H. (1995),
  ``Approximating the bandwidth for asteroidal triple-free graphs'',
  Proc. 3rd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 979, Springer-Verlag, 434-447.
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310
  Ko, M. T., Lee, R. C. T., and Chang, J. S. (1990),
  ``An optimal approximation algorithm for the rectilinear m-center problem'',
  Algorithmica 5, 341-352.
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311
  Kohli, R., Krishnamurti, R., and Mirchandani, P. (1994),
  ``The minimum satisfiability problem'',
  SIAM J. Disc. Math. 7, 275-283.
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312
  Kolaitis, P. G., and Thakur, M. N. (1994),
  ``Logical definability of NP optimization problems'',
  Inform. and Comput. 115, 321-353.
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313
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  ``Approximation properties of NP minimization classes'',
  J. Comput. System Sci. 50, 391-411.
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314
  Kolliopoulos, S. G., and Stein, C. (1997),
  ``Improved approximation algorithms for unsplittable flow problems'',
  Proc. 38th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 426-435.
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315
  Kortsarz, G. (1998),
  ``On the hardness of approximating spanners'',
  Proc. 1st Int. Workshop on Approximation Algorithms for Combinatorial Problems, , Lecture Notes in Comput. Sci., Springer-Verlag, 135-146.
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316
  Kortsarz, G., and Peleg, D. (1992),
  ``Generating sparse 2-spanners'',
  Proc. 3rd Scandinavian Workshop on Algorithm Theory, Lecture Notes in Comput. Sci. 621, Springer-Verlag, 73-82.
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317
  Kortsarz, G., and Peleg, D. (1993),
  ``On choosing a dense subgraph'',
  Proc. 34th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 692-701.
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318
  Kortsarz, G., and Peleg, D. (1994),
  ``Generating low-degree 2-spanners'',
  Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 556-563.
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319
  Kortsarz, G., and Peleg, D. (1995),
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  SIAM J. Disc. Math. 8, 401-427.
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320
  Kortsarz, G., and Peleg, D. (1997),
  ``Approximating shallow-light trees'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 103-110.
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321
  Kosaraju, S. R., Park, J. K., and Stein, C. (1994),
  ``Long tours and short superstrings'',
  Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 166-177.
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322
  Kou, L. T., Stockmeyer, L. J., and Wong, C. K. (1978),
  ``Covering edges by cliques with regard to keyword conflicts and intersection graphs'',
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323
  Koutsoupias, E., Papadimitriou, C. H., and Yannakakis, M. (1996),
  ``Searching a fixed graph'',
  Proc. 23rd Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1099, Springer-Verlag, 280-289.
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324
  Krivelevich, M., and Sudakov, B. (1998),
  ``Approximate coloring of uniform hypergraphs'',
  Proc. 6th Ann. European Symp. on Algorithms, , Lecture Notes in Comput. Sci., Springer-Verlag, 477-489.
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325
  Krumke, S. O. (1995),
  ``On a generalization of the p-center problem'',
  Inform. Process. Lett. 56, 67-71.
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326
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  ``Improving spanning trees by upgrading nodes'',
  Proc. 24th Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1256, Springer-Verlag, 281-291.
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327
  Kumar, V. (1998),
  ``Approximating circular arc colouring and bandwidth allocation in all-optical ring networks'',
  Proc. 1st Int. Workshop on Approximation Algorithms for Combinatorial Problems, , Lecture Notes in Comput. Sci., Springer-Verlag, 147-158.
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328
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  SIAM J. Comp. 6, 518-536.
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329
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330
  Lenstra, J. K., and Kan, A. H. G. Rinnooy (1978),
  ``Complexity of scheduling under precedence constraints'',
  Oper. Res. 26, 22-35.
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331
  Lenstra, J. K., and Shmoys, D. B. (1995),
  ``Computing near-optimal schedules'', in
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332
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  Math. Programming 46, 259-271.
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333
  Leonardi, S., and Raz, D. (1997),
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  Proc. 29th Ann. ACM Symp. on Theory of Comp., ACM, 110-119.
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334
  Leung, J. Y.-T., and Wei, W.-D. (1995),
  ``Tighter bounds on a heuristic for a partition problem'',
  Inform. Process. Lett. 56, 51-57.
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335
  Levcopoulos, C., and Gudmundsson, J. (1997),
  ``Approximation algorithms for covering polygons with squares and similar problems'',
  Proc. 1st Symp. on Randomization and Approximation Techniques in Comput. Sci., Lecture Notes in Comput. Sci. 1269, Springer-Verlag, 27-31.
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336
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  ``The complexity of finding two disjoint paths with min-max objective function'',
  Disc. Appl. Math. 26, 105-115.
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337
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  ``On the minimum-cardinality-bounded-diameter and the bounded-cardinality-minimum-diameter edge addition problems'',
  Oper. Res. Lett. 11, 303-308.
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338
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  ``On three-dimensional packing'',
  SIAM J. Comp. 19, 847-867.
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339
  Li, M. (1990),
  ``Towards a DNA sequencing theory'',
  Proc. 31st Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 125-134.
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340
  Lin, C. (1994),
  ``Hardness of approximating graph transformation problem'',
  Proc. 5th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 834, Springer-Verlag, 74-82.
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341
  Lin, J-H., and Vitter, J. S. (1992),
  ``-approximations with minimum packing constraint violation'',
  Proc. 24th Ann. ACM Symp. on Theory of Comp., ACM, 771-782.
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342
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  ``A separator theorem for planar graphs'',
  SIAM J. Appl. Math. 36, 177-189.
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343
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  ``The power of local optimization: Approximation algorithms for maximum-leaf spanning tree'',
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344
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  ``Scheduling malleable and nonmalleable parallel tasks'',
  Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 167-176.
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345
  Lund, C., and Yannakakis, M. (1993),
  ``The approximation of maximum subgraph problems'',
  Proc. 20th Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 700, Springer-Verlag, 40-51.
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346
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  J. ACM 41, 960-981.
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347
  Mahajan, S., and Ramesh, J. (1995),
  ``Derandomizing semidefinite programming based approximation algorithms'',
  Proc. 36th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 162-169.
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348
  Makedon, F., and Tragoudas, S. (1990),
  ``Approximating the minimum net expansion: near optimal solutions to circuit partitioning problems'',
  Proc. 16th Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 484, Springer-Verlag, 140-153.
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349
  Malesinska, E., and Panconesi, A. (1996),
  ``On the hardness of frequency allocation for hybrid networks'',
  Proc. 22nd Workshop on Graph-Theoretic Concepts in Computer Science, Lecture Notes in Comput. Sci. 1197, Springer-Verlag, 308-322.
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350
  Marathe, M. V., Breu, H., Hunt III, H. B., Ravi, S. S., and Rosenkrantz, D. J. (1995),
  ``Simple heuristics for unit disk graphs'',
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351
  Marathe, M. V., Hunt III, H. B., and Ravi, S. S. (1996),
  ``Efficient approximation algorithms for domatic partition and on-line coloring of circular arc graphs'',
  Disc. Appl. Math. 64, 135-149.
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352
  Marathe, M. V., Ravi, R., Sundaram, R., Ravi, S. S., Rosenkrantz, D. J., and Hunt III, H. B. (1995),
  ``Bicriteria network design problems'',
  Proc. 22nd Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 944, Springer-Verlag, 487-498.
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353
  Maruyama, O., and Miyano, S. (1995),
  ``Graph inference from a walk for trees of bounded degree 3 is NP-complete'',
  Proc. 20th International Symp. on Mathematical Foundations of Comput. Sci., Lecture Notes in Comput. Sci. 969, Springer-Verlag, 257-266.
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354
  Mata, C. S., and Mitchell, J. S. B. (1995),
  ``Approximation algorithms for geometric tour and network design problems'',
  Proc. 11th Ann. ACM Symp. Comput. Geom., ACM, 360-369.
  (MINIMUM GEOMETRIC TRAVELING SALESPERSON, MINIMUM TRAVEL ROBOT LOCALIZATION, MINIMUM RED-BLUE SEPARATION)

355
  Michel, C., Schroeter, H., and Srivastav, A. (1995),
  ``TSP and matching in printed circuit board assembly'',
  European Symposium on Operations Research, , .
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356
  Middendorf, M. (1994),
  ``On the approximation of finding various minimal, maximal, and consistent sequences'',
  Proc. 5th Ann. Int. Symp. on Algorithms and Computation, Lecture Notes in Comput. Sci. 834, Springer-Verlag, 306-314.
  (SHORTEST COMMON SUPERSEQUENCE)

357
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  ``Computing a shortest k-link path in a polygon'',
  Proc. 33rd Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 573-582.
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358
  Mitchell, J. S. B., and Suri, S. (1992),
  ``Separation and approximation of polyhedral objects'',
  Proc. Third Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 296-306.
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359
  Möhring, R. H., Schäffter, M. W., and Schulz, A. S. (1996),
  ``Scheduling jobs with communication delays: using infeasible solutions for approximation'',
  Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 76-90.
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360
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  ``Ramsey numbers and an approximation algorithm for the vertex cover problem'',
  Acta Inf. 22, 115-123.
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361
  Motwani, R., and Naor, J. S. (1994),
  ``On exact and approximate cut covers of graphs'',
  Technical Report STAN-CS-TN-94-11, Department of Computer Science, Stanford University.
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362
  Naor, J., and Zosin, L. (1997),
  ``A 2-approximation algorithm for the directed multiway cut problem'',
  Proc. 38th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 548-553.
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363
  Natanzon, A., Shamir, R., and Sharan, R. (1998),
  ``A polynomial approximation algorithm for the minimum fill-in problem'',
  Proc. 30th Ann. ACM Symp. on Theory of Comp., ACM, 41-47.
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364
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  ``Spatial codes and the hardness of string folding problems'',
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365
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  Planar Graphs: Theory and Algorithms,
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366
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  ``On the 1.1 edge-coloring of multigraphs'',
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367
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  ``On approximation preserving reductions: Complete problems and robust measures'',
  Technical Report C-1987-28, Department of Computer Science, University of Helsinki.
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368
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  Theoretical Comput. Sci. 107, 145-163.
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369
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370
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  ``Motion planning on a graph'',
  Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 511-520.
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371
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  ``Optimization, approximation, and complexity classes'',
  J. Comput. System Sci. 43, 425-440.
  (MINIMUM VERTEX COVER, MINIMUM DOMINATING SET, MINIMUM FEEDBACK ARC SET, MAXIMUM INDEPENDENT SET, MAXIMUM K-COLORABLE SUBGRAPH, MAXIMUM CUT, MAXIMUM DIRECTED CUT, MINIMUM SET COVER, MAXIMUM SATISFIABILITY, MAXIMUM K-SATISFIABILITY, MAXIMUM NOT-ALL-EQUAL 3-SATISFIABILITY)

372
  Papadimitriou, C. H., and Yannakakis, M. (1993),
  ``The traveling salesman problem with distances one and two'',
  Math. Oper. Res. 18, 1-11.
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373
  Park, J. K., and Phillips, C. A. (1993),
  ``Finding minimum-quotient cuts in planar graphs'',
  Proc. 25th Ann. ACM Symp. on Theory of Comp., ACM, 766-775.
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374
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  ``Non deterministic polynomial optimization problems and their approximations'',
  Theoretical Comput. Sci. 15, 251-277.
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375
  Peleg, D., and Reshef, E. (1998),
  ``Deterministic polylog approximation for minimum communication spanning trees'',
  Proc. 25th Int. Colloquium on Automata, Languages and Programming, Lecture Notes in Comput. Sci. 1443, Springer-Verlag, 670-679.
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376
  Peleg, D., Schechtman, G., and Wool, A. (1993),
  ``Approximating bounded 0-1 integer linear programs'',
  Proc. 2nd Israel Symp. on Theory of Computing and Systems, IEEE Computer Society, 69-77.
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377
  Petrank, E. (1992),
  ``The hardness of approximation: gap location'',
  Technical Report 754, Computer Science Department, Technion, Israel Institute of Technology, Haifa, Israel.
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378
  Petrank, E. (1994),
  ``The hardness of approximation: gap location'',
  Computational Complexity 4, 133-157.
  (MINIMUM VERTEX COVER, MINIMUM EDGE COLORING, MAXIMUM SET SPLITTING)

379
  Phillips, C., Stein, C., and Wein, J. (1995),
  ``Scheduling jobs that arrive over time'',
  Proc. 4th Workshop on Algorithms and Data Structures, Lecture Notes in Comput. Sci. 955, Springer-Verlag, 86-97.
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380
  Phillips, C. A. (1993),
  ``The network inhibition problem'',
  Proc. 25th Ann. ACM Symp. on Theory of Comp., ACM, 776-785.
  (MINIMUM NETWORK INHIBITION ON PLANAR GRAPHS, SHORTEST WEIGHT-CONSTRAINED PATH)

381
  Pitt, L., and Warmuth, M. K. (1993),
  ``The minimum consistent DFA problem cannot be approximated within any polynomial'',
  J. ACM 40, 95-142.
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382
  Plaisted, D. A., and Hong, J. (1987),
  ``A heuristic triangulation algorithm'',
  J. Algorithms 8, 405-437.
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383
  Plesník, J. (1980),
  ``On the computational complexity of centers locating in a graph'',
  Aplikace Matematiky 25, 445-452.
  (MINIMUM K-CENTER)

384
  Plesník, J. (1981),
  ``The complexity of designing a network with minimum diameter'',
  Networks 11, 77-85.
  (MINIMUM DIAMETER SPANNING SUBGRAPH)

385
  Plesník, J. (1982),
  ``Complexity of decomposing graphs into factors with given diameters or radii'',
  Math. Slovaca 32, 379-388.
  (MINIMUM DIAMETERS DECOMPOSITION)

386
  Plesník, J. (1987),
  ``A heuristic for the p-center problem in graphs'',
  Disc. Appl. Math. 17, 263-268.
  (MINIMUM K-CENTER)

387
  Plesník, J. (1988),
  ``Two heuristics for the absolute p-center problem in graphs'',
  Math. Slovaca 38, 227-233.
  (MINIMUM K-CENTER)

388
  Provan, J. S. (1988),
  ``An approximation scheme for finding Steiner trees with obstacles'',
  SIAM J. Comp. 17, 920-934.
  (MINIMUM GEOMETRIC STEINER TREE)

389
  Queyranne, M. (1985),
  ``Bounds for assembly line balancing heuristics'',
  Oper. Res. 33, 1353-1359.
  (MINIMUM BIN PACKING)

390
  Queyranne, M. (1986),
  ``Performance ratio of polynomial heuristics for triangle inequality quadratic assignment problems'',
  Oper. Res. Lett. 4, 231-234.
  (MINIMUM QUADRATIC 0-1 ASSIGNMENT)

391
  Rabani, Y. (1996),
  ``Path coloring on the mesh'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 400-409.
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392
  Raghavan, P., and Thompson, C. D. (1991),
  ``Multiterminal global routing: A deterministic approximation scheme'',
  Algorithmica 6, 73-82.
  (MINIMUM RECTILINEAR GLOBAL ROUTING)

393
  Raghavan, P., and Upfal, E. (1994),
  ``Efficient routing in all-optical networks'',
  Proc. 26th Ann. ACM Symp. on Theory of Comp., ACM, 134-143.
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394
  Rao, S., and Richa, A. W. (1998),
  ``New approximation techniques for some ordering problems'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 211-218.
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395
  Ravi, R. (1994a),
  ``A primal-dual approximation algorithm for the Steiner forest problem'',
  Inform. Process. Lett. 50, 185-190.
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396
  Ravi, R. (1994b),
  ``Rapid rumor ramification: approximating the minimum broadcast time'',
  Proc. 35th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 202-213.
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397
  Ravi, R., Sundaram, R., Marathe, M. V., Rosenkrantz, D. J., and Ravi, S. S. (1994),
  ``Spanning trees short or small'',
  Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 546-555.
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398
  Ravi, R., and Williamson, D. (1997),
  ``An approximation algorithm for minimum-cost vertex-connectivity problems'',
  Algorithmica 18, 21-43.
  (MINIMUM K-VERTEX CONNECTED SUBGRAPH)

399
  Ravi, S. S., Rosenkrantz, D. J., and Tayi, G. K. (1991),
  ``Facility dispersion problems: heuristics and special cases'',
  Proc. 2nd Workshop on Algorithms and Data Structures, Lecture Notes in Comput. Sci. 519, Springer-Verlag, 355-366.
  (MAXIMUM K-FACILITY DISPERSION)

400
  Rayward-Smith, V. J. (1987),
  ``Net scheduling with unit interprocessor communication delays'',
  Disc. Appl. Math. 18, 55-71.
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401
  Raz, R., and Safra, S. (1997),
  ``A sub-constant error-probability low-degree test, and sub-constant error-probability pcp characterization of np'',
  Proc. 29th Ann. ACM Symp. on Theory of Comp., ACM, 475-484.
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402
  S. Nicoloso, X. Song, M. Sarrafzadeh (1994),
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  Technical Report R. 390, Istituto di Analisi dei Sistemi ed Informatica (IASI-CNR).
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403
  Sahni, S. K., and Gonzalez, T. F. (1976),
  ``P-complete approximation problems'',
  J. ACM 23, 555-565.
  (MINIMUM VERTEX DISJOINT CYCLE COVER, MINIMUM EDGE DISJOINT CYCLE COVER, MINIMUM EDGE DELETION K-PARTITION, MINIMUM K-CLUSTERING SUM, MINIMUM GENERALIZED 0-1 ASSIGNMENT, MINIMUM QUADRATIC 0-1 ASSIGNMENT)

404
  Salman, F. S., Cheriyan, J., Ravi, R., and Subramanian, S. (1997),
  ``Buy-at-bulk network design: approximating the single-sink edge installation problem'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 619-628.
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405
  Saran, H., and Vazirani, V. (1991),
  ``Finding k-cuts within twice the optimal'',
  Proc. 32nd Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 743-751.
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406
  Savage, Carla (1982),
  ``Depth-first search and the vertex cover problem'',
  Inform. Process. Lett. 14, 233-237.
  (MINIMUM VERTEX COVER)

407
  Schiermeyer, I. (1994),
  ``Reverse-fit: a 2-optimal algorithm for packing rectangles'',
  Proc. 2nd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 855, Springer-Verlag, 290-299.
  (MINIMUM HEIGHT TWO DIMENSIONAL PACKING)

408
  Schulz, A. S., and Skutella, M. (1996),
  ``Scheduling-LPs bear probabilities: Randomized approximations for Min-sum criteria'',
  Technical Report 533/1996, Technical University of Berlin, Department of Mathematics.
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409
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  ``Scheduling-LPs bear probabilities: randomized approximation for Min-sum criteria'',
  Proc. 5th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1284, Springer-Verlag, 416-429.
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410
  Schulz, A. S., and Skutella, M. (1997b),
  ``Random-based scheduling: New approximations and LP lower bounds'',
  Proc. 1st Symp. on Randomization and Approximation Techniques in Comput. Sci., Lecture Notes in Comput. Sci. 1269, Springer-Verlag, 119-133.
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411
  Serdyukov, A. I. (1984),
  ``An algorithm with an estimate for the traveling salesman problem of the maximum'',
  Upravlyaemye Sistemy 25, 80-86.
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412
  Seymour, P. D. (1995),
  ``Packing directed circuits fractionally'',
  Combinatorica 15, 281-288.
  (MINIMUM FEEDBACK VERTEX SET)

413
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  Combinatorica 14, 217-241.
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414
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415
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  ``The maximum subforest problem: Approximation and exact algorithms'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 394-399.
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416
  Shmoys, D. B. (1997),
  ``Cut problems and their application to divide-and-conquer'', in
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417
  Shmoys, D. B., Stein, C., and Wein, J. (1994),
  ``Improved approximation algorithms for shop scheduling problems'',
  SIAM J. Comp. 23, 617-632.
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418
  Shmoys, D. B., and Tardos, É. (1993),
  ``Scheduling unrelated machines with costs'',
  Proc. 4th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 448-454.
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419
  Simchi-Levi, D. (1994),
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  Naval Res. Logistics 41, 579-585.
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420
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  ``Approximation algorithms for channel assignment in cellular radio networks'',
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421
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  SIAM J. Disc. Math. 3, 294-310.
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422
  Skutella, M. (1997),
  ``Approximation algorithms for the discrete time-cost tradeoff problem'',
  Proc. 8th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 501-508.
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423
  Srinivasan, A. (1995),
  ``Improved approximations of packing and covering problems'',
  Proc. 27th Ann. ACM Symp. on Theory of Comp., ACM, 268-276.
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424
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  Proc. 38th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 416-425.
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425
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  ``Tight approximations for resource constrained scheduling problems'',
  Proc. 2nd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 855, Springer-Verlag, 307-318.
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426
  Tamir, A. (1991),
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  SIAM J. Disc. Math. 4, 550-567.
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427
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  Theoretical Comput. Sci. 57, 131-145.
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428
  Trevisan, L. (1996),
  ``Positive linear programming, parallel approximation and PCPs'',
  Proc. 4th Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 1136, Springer-Verlag, 62-75.
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429
  Trevisan, L. (1997),
  ``When Hamming meets Euclid: the approximability of geometric TSP and MST'',
  Proc. 29th Ann. ACM Symp. on Theory of Comp., ACM, 21-29.
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430
  Trevisan, L., Sorkin, G. B., Sudan, M., and Williamson, D. P. (1996),
  ``Gadgets, approximation, and linear programming'',
  Proc. 37th Ann. IEEE Symp. on Foundations of Comput. Sci., IEEE Computer Society, 617-626.
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431
  Turek, J., Schwiegelshohn, U., Wolf, J. L., and Yu, P. S. (1994),
  ``Scheduling parallel tasks to minimize average response time'',
  Proc. 5th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 112-121.
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432
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  ``Approximation algorithms for the shortest common superstring problem'',
  Inform. and Comput. 83, 1-20.
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433
  Verbitsky, O. (1994),
  ``On the largest common subgraph problem'',
  Unpublished manuscript.
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434
  Verbitsky, O. (1995),
  ``On the hardness of approximating some optimization problems that are supposedly easier than Max Clique'',
  Combinatorics, Probability and Computing 4, 167-180.
  (MAXIMUM H-MATCHING, MAXIMUM INDEPENDENT SET, MAXIMUM K-CONSTRAINT SATISFACTION)

435
  Vishwanathan, S. (1992),
  ``An approximation algorithm for the asymmetric travelling salesman problem with distances one and two'',
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436
  Vishwanathan, S. (1996),
  ``An approximation algorithm for the asymmetric p-center problem'',
  Proc. 7th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 1-5.
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437
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  ``Personal communication'',
  Unpublished manuscript.
  (MAXIMUM INDEPENDENT SET)

438
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  Diskret. Analiz. 3, 23-30.
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439
  Wagner, F., and Wolff, A. (1995),
  ``An efficient and effective approximation algorithm for the map labeling problem'',
  Proc. 3rd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 979, Springer-Verlag, 420-433.
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440
  Wang, Q., and Cheng, K. H. (1990),
  ``A heuristic algorithm for the k-center problem with cost and usage weights'',
  Technical Report TR #UH-CS-90-15, Computer Science Department, Houston University.
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441
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  ``Assembly line balancing as generalized bin packing'',
  Oper. Res. Lett. 1, 56-58.
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442
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  ``A primal-dual approximation algorithm for generalized Steiner network problems'',
  Combinatorica 15, 435-454.
  (MINIMUM GENERALIZED STEINER NETWORK)

443
  Williamson, D. P., Hall, L. A., Hoogeveen, J. A., Hurkens, C. A. J., Lenstra, J. K., and Shmoys, D. B. (1994),
  ``Short shop schedules'',
  Unpublished manuscript.
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444
  Wöginger, G. J., and Yu, Z. (1992),
  ``A heuristic for preemptive scheduling with set-up times'',
  Computing 49, 151-158.
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445
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  ``Exact and approximation algorithms for constructing ultrametric trees from distance metrics'',
  Proc. 4th Ann. Int. Conf. on Computing and Combinatorics, Lecture Notes in Comput. Sci. 1449, Springer-Verlag, 299-308.
  (MINIMUM SIZE ULTRAMETRIC TREE)

446
  Wu, B. Y., Lancia, G., Bafna, V., Chao, K., Ravi, R., and Tang, C. Y. (1998),
  ``A polynomial time approximation scheme for Minimum routing cost spanning tree'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 21-32.
  (MINIMUM COMMUNICATION COST SPANNING TREE, MINIMUM TREE ALIGNMENT)

447
  Yannakakis, M. (1979),
  ``The effect of a connectivity requirement on the complexity of maximum subgraph problems'',
  J. ACM 26, 618-630.
  (MINIMUM VERTEX DELETION TO OBTAIN CONNECTED SUBGRAPH WITH PROPERTY P)

448
  Yannakakis, M., and Gavril, F. (1980),
  ``Edge dominating sets in graphs'',
  SIAM J. Appl. Math. 38, 364-372.
  (MINIMUM MAXIMAL MATCHING)

449
  Yu, B., and Cheriyan, J. (1995),
  ``Approximation algorithms for feasible cut and multicut problems'',
  Proc. 3rd Ann. European Symp. on Algorithms, Lecture Notes in Comput. Sci. 979, Springer-Verlag, 394-408.
  (MINIMUM MULTI-CUT)

450
  Yue, M. (1991),
  ``A simple proof of the inequality for the MFFD bin-pack algorithm'',
  Technical Report RRR # 20-91, Rutcor, Rutgers Center for Operations Research, Rutgers University, New Jersey.
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451
  Zhang, K., and Jiang, T. (1994),
  ``Some MAX SNP-hard results concerning unordered labeled trees'',
  Inform. Process. Lett. 49, 249-254.
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452
  Zuckerman, D. (1993),
  ``NP-complete problems have a version that's hard to approximate'',
  Proc. Eight Ann. Structure in Complexity Theory Conf., IEEE Computer Society, 305-312.
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453
  Zwick, U. (1998),
  ``Approximation algorithms for constraint satisfaction problems involving at most three variables per constraint'',
  Proc. 9th Ann. ACM-SIAM Symp. on Discrete Algorithms, ACM-SIAM, 201.
  (MAXIMUM NOT-ALL-EQUAL 3-SATISFIABILITY, MAXIMUM K-CONSTRAINT SATISFACTION)