ISBN: 3540661514
TITLE: Constraint Databases
AUTHOR: Kuper, Gabriel; Libkin, Leonid; Paredaens, Jan (Eds.)
TOC:

1. Introduction 1
Gabriel Kuper, Leonid Libkin, and Jan Paredaens
1.1 Motivation and Framework 1
1.2 Relational Databases and First-Order Query Languages 2
1.3 Spatial Data 4
1.4 Constraint Databases 7
1.5 The CDB Model 8
1.6 Querying Constraint Databases 10
1.7 Applications 13
1.8 Historical Note 15
Part I. Theoretical Foundations
2. Constraint Databases, Queries, and Query Languages 21
Jan Van den Bussche
2.1 Introduction 21
2.2 Logic 21
2.2.1 Quantifier Elimination 23
2.3 The Constraint Database Model 23
2.3.1 Constraints 23
2.3.2 Constraint Databases 25
2.3.3 Testing Equality of Constraint Relations 27
2.4 Queries on Constraint Databases 28
2.4.1 Constraint Queries 28
2.4.2 Relational Calculus with Constraints 30
2.4.3 Computational Feasibility 33
2.4.4 Relational Algebra with Constraints 34
2.5 Computationally Complete Constraint Query Languages 35
2.6 Equivalence and Satisfiability 39
2.7 Conjunctive Queries with Constraints 43
2.8 Datalog with Constraints 47
2.8.1 Adding Negation 51
2.9 Bibliographic Notes 53
3. Expressive Power: The Finite Case 55
Michael Benedikt and Leonid Libkin
3.1 Introduction 55
3.1.1 Semantics of Constraint Queries 56
3.1.2 Collapse Results 57
3.2 Notation 60
3.2.1 Relational Databases over Infinite Structures 60
3.2.2 First-Order Logic 61
3.2.3 Genericity 62
3.3 Active Semantics 62
3.4 Natural Semantics 66
3.4.1 Natural-Active Collapse 66
3.4.2 O-Minimality 68
3.4.3 Natural-Active Collapse: Algorithm and Proof 69
3.4.4 When the Collapse Fails 73
3.5 Higher-Order Logics 74
3.5.1 Natural Semantics and Hybrid Logics 77
3.6 Other Techniques and Extensions 79
3.7 Conclusion 84
3.8 Bibliographic Notes 84
4. Expressive Power: The Infinite Case 89
Stphane Grumbach, Gabriel Kuper, and Jianwen Su
4.1 Introduction 89
4.2 Complexity of First-Order Queries 89
4.2.1 FO+Poly 90
4.2.2 Encoding of Boolean Circuits 92
4.2.3 FO+Lin 94
4.2.4 FO+Lin over Restricted Databases 97
4.2.5 FO(<) 98
4.3 Expressive Power of First-Order Queries 98
4.4 Expressive Power of Recursive Languages 102
4.4.1 Datalog (<) 102
4.4.2 Datalog + lin 104
4.5 Bibliographic Notes 106
5. Query Safety with Constraints 109
Michael Benedikt and Leonid Libkin
5.1 Introduction 109
5.2 Safe Constraint Queries: The Finite Case 111
5.2.1 Preliminaries 111
5.2.2 Safe Translations 112
5.2.3 Range-Restriction and Safety 114
5.2.4 Deciding Safety 118
5.2.5 Dichotomy Theorem and Outputs of Queries 120
5.3 Safe Constraint Queries: The Infinite Case 121
5.3.1 Preserving Geometric Properties 121
5.3.2 Safety via Coding 122
5.3.3 Examples of Coding 123
5.3.4 Decidability Results and Geometric Bounds 126
5.4 Bibliographic Notes 127
6. Aggregate Languages for Constraint Databases 131
Jan Chomicki and Leonid Libkin
6.1 Introduction 131
6.2 Relational and Spatial Aggregation 132
6.3 Approximating the Volume 136
6.4 Definability of Volume Operators 140
6.5 Restricted Aggregate Operators 144
6.5.1 Variable Independence and Closure 145
6.5.2 FO+Poly + Sum and Volumes of Semi-Linear Sets 148
6.6 Conclusion 152
6.7 Bibliographic Notes 153
7. Datalog and Constraints 155
Peter Z. Revesz
7.1 Introduction 155
7.2 Evaluation of Datalog with Constraints 155
7.3 Termination, Safety, and Data Complexity 156
7.4 Datalog with Dense Order Constraints 156
7.5 Datalog with Gap-Order Constraints 158
7.5.1 General Theory 158
7.5.2 Stratified Datalog with Gap-Order Constraints 159
7.5.3 Datalog with Unrestricted Gap-Order Constraints 162
7.6 Datalog with Linear Constraints 163
7.7 Datalog with Polynomial Constraints 163
7.8 Datalog with Boolean Equality Constraints 167
7.8.1 General Theory 167
7.8.2 Application: Adder Circuit 168
7.9 Bibliographic Notes 169
Part II. Spatial and Temporal Data
8. Geographic Information Systems 175
Gabriel Kuper and Michel Scholl
8.1 Introduction 175
8.1.1 What is Geographic Information? 175
8.1.2 Are GIS DBMS for Geographic Information? 176
8.1.3 Geographic Data Sources 176
8.1.4 GIS Applications 177
8.1.5 Which Spatial Operations are Expected From a GIS? 177
8.1.6 Brief History of GIS 179
8.2 GIS Data Models 180
8.2.1 Vector vs. Raster Data 181
8.2.2 Spatial Models and Representation of Topology 182
8.2.3 Sample Spatial Database Schema 185
8.2.4 Examples of Queries 186
8.2.5 Limitations of the Current Models 187
8.3 The Constraint Approach for GIS 187
8.4 Representing Spatial Data with Constraints 188
8.4.1 Conversion 188
8.4.2 Storage 190
8.4.3 The Constraint vs. the Vector Approach 191
8.5 Queries over Constraint Databases 192
8.6 Role of Constraints in a GIS 196
8.7 Bibliographic Notes 197
9. Linear-Constraint Databases 199
Marc Gyssens, Luc Vandeurzen, and Dirk Van Gucht
9.1 Introduction 199
9.2 Properties of Semi-Linear Sets 200
9.3 Positive Expressiveness Results 201
9.4 Negative Expressiveness Results 208
9.5 Extensions of FO+Lin 212
9.5.1 Extensions of FO+Lin with Operators 213
9.5.2 Extension of FO+Lin with Product Variables 214
9.5.3 Finite Representations of Semi-Linear Sets 217
9.5.4 Complete Languages for FO+Poly-Expressible
Linear Queries 226
9.5.5 Complete Languages for Linear Queries 227
9.6 Bibliographic Notes 227
10. Topological Queries 231
Bart Kuijpers and Victor Vianu
10.1 Introduction 231
10.2 Preliminaries 234
10.3 Languages for Topological Queries 236
10.3.1 The 4-Intersection Relations 236
10.3.2 Region-Based Languages 239
10.3.3 Topological Elementary Equivalence 249
10.4 Topological Invariants 257
10.4.1 Lossless Topological Invariants 257
10.4.2 Spatial Representations of Topological Information 261
10.5 Using Topological Invariants to Answer Topological Queries 261
10.5.1 Fixpoint Queries on Topological Invariants 262
10.5.2 Translating Spatial Queries to Queries on the
Invariant 265
10.6 Bibliographic Notes 271
11. Euclidean Query Languages 275
Bart Kuijpers, Gabriel Kuper, and Jan Paredaens
11.1 Introduction 275
11.2 Semi-Circular Relations 277
11.3 Query Language over Encodings of Semi-Circular Relations 279
11.4 Safe Restriction of the Language 282
11.5 Languages for Semi-Circular Relations 283
11.5.1 Definition of the Query Language 284
11.5.2 Comparison with FO+Lin 286
11.5.3 Comparison with FO+Poly 288
11.6 Conclusion 290
11.7 Bibliographic Notes 290
12. Genericity in Spatial Databases 293
Bart Kuijpers and Dirk Van Gucht
12.1 Introduction 293
12.2 Definitions and Examples 294
12.3 Undecidability Results 297
12.4 Sound and Complete Languages for Generic Queries 298
12.4.1 FO+Poly 298
12.4.2 Computable Queries 301
12.5 Bibliographical Notes 302
13. Linear Repeating Points 305
Pierre Wolper
13.1 Introduction 305
13.2 A Constraint Model of Temporal Databases 306
13.2.1 Expressiveness of the Model 307
13.3 Computing with Temporal Constraints 308
13.3.1 A First Approach 308
13.3.2 Finite Automata as Constraints 309
13.3.3 Computing with Lrps Represented by Automata 312
13.4 Bibliographic Notes 313
Part III. Algorithmic Aspects
14. Optimization Techniques 319
Stphane Grumbach, Zo Lacroix, Philippe Rigaux,
and Luc Segoufin
14.1 Introduction 319
14.2 Spatial Query Processing and Optimization 320
14.2.1 Data Modeling 320
14.2.2 Query Languages 321
14.2.3 Query Processing 321
14.2.4 Query Optimization 322
14.3 Impact of the Data Format 323
14.3.1 Constraint Clustering 323
14.3.2 Orthographic Dimension 325
14.4 Query Processing 328
14.4.1 Alternation of Computation Modes 329
14.4.2 Query Pattern Recognition 330
14.5 Bibliographic Notes 333
15. Constraint Algebras 335
Dina Goldin
15.1 Introduction 335
15.2 FO(<) 335
15.2.1 Data Representation 335
15.2.2 Canonical Form 336
15.3 Monotone Two-Variable Constraints 339
15.4 Bibliographic Notes 342
16. I/O-Efficient Algorithms for CDBs 343
Sridhar Ramaswamy
16.1 Introduction 343
16.2 Dynamic Interval Management in Secondary Memory 345
16.2.1 Efficient Static Data Structure for Stabbing Queries 345
16.2.2 Dynamic Interval Management 348
16.2.3 Practical Aspects of Indexing Constraints 351
16.3 Constraint Join 352
16.3.1 One-Dimensional Join 352
16.3.2 Two-Dimensional Case: Rectangle Join 353
16.3.3 Practical Aspects of the Join 356
16.4 Lower Bounds 357
16.5 Conclusion 359
16.6 Bibliographic Notes 359
Part IV. Prototypes
17. The DEDALE Prototype 365
Stphane Grumbach, Philippe Rigaux, Michel Scholl, and Luc Segoufin
17.1 Introduction 365
17.2 The Data Model 366
17.3 Constraint Representation and Storage with O_2 368
17.3.1 Data Conversion: Loading and Displaying 369
17.4 The Query Language 371
17.5 Query Processing 375
17.5.1 Translation, Rewriting, and Evaluation 375
17.5.2 Constraint Manipulation 377
17.5.3 Implementation of Algebraic Operators 379
17.6 Conclusion 380
17.7 Bibliographic Notes 381
18. The DISCO System 383
Peter Revesz
18.1 Introduction 383
18.2 DISCO Queries 383
18.3 Implementation 384
18.3.1 Converting to Relational Algebra 384
18.3.2 Optimization of Relational Algebra 386
18.4 Extensibility of DISCO 388
18.5 Bibliographic Notes 388
19. SQL/TP: A Temporal Extension of SQL 391
David Toman
19.1 Introduction 391
19.2 Temporal Data Model and Constraint Encoding 391
19.2.1 Representable Temporal Databases 392
19.2.2 Data Definition Language 392
19.3 Queries 393
19.3.1 Syntax and Semantics 394
19.3.2 Query Compilation 395
19.4 Bibliographic Notes 398
Bibliography 401
Index 423
List of Contributors
Michael Benedikt, Bell Labs/Lucent Technologies, 263 Shuman Blvd., PO Box 3050, Naperville, IL 60566, USA, benedikt@bell-labs.com
Jan Chomicki, Dept. of Computer Science, Monmouth University, Howard Hall, West Long Branch, NJ 07764, USA, chomicki@monmouth.edu
Dina Goldin, Dept. of Math. and CS, UMASS-Boston, 100 Morrissey Blvd., Boston, MA 02125, USA, dqg@cs.umb.edu
Stphane Grumbach, INRIA, Rocquencourt BP105, 78153 Le Chesnay Cedex, France
Stephane.Grumbach@inria.fr, Marc Gyssens, University of Limburg (LUC), Dept. WNI, Universitaire Campus, 3590 Diepenbeek, Belgium, gyssens@charlie.luc.ac.be
Bart Kuijpers, University of Limburg (LUC), Dept. WNI, Universitaire Campus, 3590 Diepenbeek, Belgium, bart.kuijpers@luc.a.be
Zo Lacroix, Data Logic, A Division of Gene Logic Inc., 2001 Center Street, Suite 600, Berkeley, CA 94704, USA, zlacroix@genelogic.com
Sridhar Ramaswamy, Bell Labs/Lucent Technologies, 600 Mountain Ave., Murray Hill, NJ 07974, USA, sridhar@bell-labs.com
Peter Revesz, Dept. of Comp. Sci. and Eng., University of Nebraska-Lincoln, Lincoln, NE 68588, USA, revesz@cse.unl.edu
Philippe Rigaux, Cedric/CNAM, 292, rue St. Martin, 75141 Paris Cedex 03, France, rigaux@cnam.fr
Michel Scholl, Cedric/CNAM, 292, rue St. Martin, 75141 Paris Cedex 03, France and INRIA Rocquencourt BP105, 78153 Le Chesnay Cedex, France, Michel.Scholl@inria.fr
Luc Segoufin, INRIA, Rocquencourt BP105, 78153 Le Chesnay Cedex, France, Luc.Segoufin@inria.fr
Jianwen Su, Dept. of Computer Science, University of California, Santa Barbara, CA 93106, USA, su@cs.ucsb.edu
David Toman, Dept. of Computer Science, 200 University Avenue West, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada, david@algonquin.uwaterloo.ca
Jan Van den Bussche, University of Limburg (LUC), Dept. WNI, Universitaire Campus, 3590 Diepenbeek, Belgium, jbussche@cs.ucsd.edu
Luc Vandeurzen, University of Limburg (LUC), Dept. WNI, Universitaire Campus, 3590 Diepenbeek, Belgium, lvdeurze@luc.ac.be
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