ISBN: 3-540-64505-5
TITLE: Universal Routing Strategies for Interconnection Networks
AUTHOR: Scheideler, Christian (Ed.)
TOC:

1. Introduction 1 
1.1 The Emergence of Parallel Systems 1 
1.2 Theoretical Research in Parallel Computing 2 
1.3 History of Routing 4 
1.4 Research Areas related to Routing 8 
1.4.1 Parallel Sorting 8 
1.4.2 Shop Scheduling 9 
1.4.3 Multicommodity Flow 10 
1.4.4 Network Emulations 10 
1.4.5 Shared Memory Simulations 11 
1.4.6 Load Balancing 12 
1.5 Main Contributions of this Book 13 
2. Communication Mechanisms Used in Practice 15 
2.1 Multiplexing 15 
2.2 Switching Elements 16 
2.2.1 Circuit Switches 16 
2.2.2 Packet Switches 17 
2.3 Local Area Networks (LAN) 18 
2.3.1 The Ethernet 18 
2.3.2 The Fibre Distributed Data Interface (FDDI) 19 
2.4 Wide Area Networks (WAN) 20 
2.4.1 The Synchronous Digital Hierarchy (SDH) 20 
2.4.2 The Asynchronous Transfer Mode (ATM) 21 
2.5 Communication Systems for Parallel Computers 23 
2.5.1 Non-scalable Parallel Computers 23 
2.5.2 Scalable Parallel Computers 24 
2.6 The OSI Model 24 
3. Terminology 27 
3.1 Basic Definitions and Inequalities 27 
3.2 Basic Definitions in Probability Theory 28 
3.3 Basic Definitions in Graph Theory 29 
3.4 Basic Definitions in Routing Theory 30 
3.4.1 The Hardware Model 31 
3.4.2 The Routing Problem 34 
3.4.3 Message Passing Models 35 
3.4.4 Routing Strategies 36 
3.4.5 Space-Efficient Routing 38 
4. Introduction to Store-and-Forward Routing 41 
4.1 History of Store-and-Forward Routing 41 
4.1.1 Routing in Specific Networks 42 
4.1.2 Universal Routing 43 
4.2 Optimal Networks for Permutation Routing 44 
4.2.1 Optimal Networks for Randomized Routing 45 
4.2.2 Optimal Networks for Deterministic Routing 45 
5. The Routing Number 47 
5.1 Existence of Efficient Path Systems 48 
5.2 Valiant's Trick 50 
5.3 The Routing Number of Specific Networks 52 
5.4 Routing Number vs. Expansion 53 
5.5 Computing Efficient Path Systems 54 
5.5.1 An Algorithm for Arbitrary Networks 54 
5.5.2 An Algorithm for Node-Symmetric Networks 55 
5.6 Summary of Main Results 55 
6. Offline Routing Protocols 57 
6.1 Keeping the Routing Time Low 58 
6.2 Keeping the Buffer Size Low 62 
6.3 Applications 67 
6.3.1 Network Emulations Using 11 Embeddings 67 
6.3.2 Network Emulations Using 1Many Embeddings 68 
6.4 Summary of Main Results 70 
7. Oblivious Routing Protocols 73 
7.1 The Random Delay Protocol 73 
7.1.1 Description of the Protocol 73 
7.1.2 Applications 75 
7.1.3 Limitations 75 
7.2 The Random Rank Protocol 75 
7.2.1 Description of the Protocol 75 
7.2.2 Applications 78 
7.2.3 Limitations 80 
7.3 Ranade's Protocol 82 
7.3.1 Description of the Protocol 82 
7.3.2 Applications 84 
7.3.3 Limitations 84 
7.4 The Growing Rank Protocol 84 
7.4.1 Description of the Protocol 85 
7.4.2 Applications 89 
7.4.3 Limitations 90 
7.5 The Extended Growing Rank Protocol 91 
7.5.1 Description of the Protocol 91 
7.5.2 Applications 95 
7.5.3 Limitations 98 
7.6 The Trial-and-Failure Protocol 98 
7.6.1 Description of the Protocol 99 
7.6.2 Applications 101 
7.6.3 Limitations 102 
7.7 The Duplication Protocol 102 
7.7.1 Description of the Protocol 103 
7.7.2 Applications 105 
7.7.3 Limitations 106 
7.8 The Protocol by Rabani and Tardos 106 
7.8.1 Description of the Protocol 106 
7.8.2 Applications 110 
7.8.3 Limitations 110 
7.9 The Protocol by Ostrovsky and Rabani 111 
7.9.1 Description of the Protocol 111 
7.9.2 Applications 111 
7.9.3 Limitations 112 
7.10 Summary of Main Results 112 
8. Adaptive Routing Protocols 115 
8.1 Deterministic Routing in Multibutterflies 116 
8.1.1 The r-replicated s-ary Multibutterfly 116 
8.1.2 Description of the Simple Protocol 117 
8.1.3 Analysis of the Simple Protocol 118 
8.1.4 Description of the Global Protocol 129 
8.1.5 Analysis of the Global Protocol 131 
8.2 Universal Adaptive Routing Strategies 134 
8.2.1 Greedy Routing Strategies 134 
8.2.2 Routing via Sorting 135 
8.2.3 Routing via Simulation135 
8.3 Summary of Main Results 138 
9. Compact Routing Protocols 139 
9.1 History of Compact Routing 139 
9.1.1 Relationship between Space and Stretch Factor 139 
9.1.2 Relationship between Space and Slowdown 142 
9.2 The "Routing via Simulation" Strategy 143 
9.2.1 Selecting Suitable Routing Structures 143 
9.2.2 Space-Efficient Perfect Hashing 145 
9.2.3 Design of Compact Routing Tables 145 
9.3 Randomized Compact Routing 147 
9.3.1 The (s, d, k)-Butterfly 147 
9.3.2 The Simulation Strategy 148 
9.3.3 Bounding the Congestion and Dilation 151 
9.3.4 Applications 154 
9.4 Deterministic Compact Routing 155 
9.4.1 The Simulation Strategy 157 
9.4.2 Applications 160 
9.5 Summary of Main Results 160 
10. Introduction to Wormhole Routing 163 
10.1 History of Wormhole Routing 164 
10.1.1 Routing in Specific Networks 164 
10.1.2 Universal Routing 165 
10.2 Upper and Lower Bounds 166 
11. Oblivious Routing Protocols 167 
11.1 The Trial-and-Failure Protocol 167 
11.1.1 Wormhole Routing in Meshes and Tori 168 
11.1.2 Wormhole Routing in Butterflies 169 
11.1.3 Further Applications 175 
11.2 The Duplication Protocol 176 
11.3 Summary of Main Results 177 
12. Protocols for All-Optical Networks 179 
12.1 An All-Optical Hardware Model 179 
12.2 Overview on All-Optical Routing 180 
12.3 A Simple, Efficient Protocol 182 
12.3.1 Applications 185 
12.4 Proof of Theorems 12.3.1 and 12.3.3 186 
12.4.1 The Upper Bound 186 
12.4.2 The Lower Bound 193 
12.5 Proof of Theorem 12.3.2 201 
12.5.1 The Upper Bound 201 
12.5.2 The Lower Bound 207 
13. Summary and Future Directions 209 
13.1 Store-and-Forward Routing 209 
13.1.1 Path Selection 210 
13.1.2 Offline Routing 210 
13.1.3 Oblivious Routing 211 
13.1.4 Adaptive Routing 212 
13.1.5 Compact Routing 212 
13.2 Wormhole Routing 213 
13.3 Future Directions 214 
13.3.1 Dynamic Routing 214 
13.3.2 Routing in Faulty and Dynamic Networks 216 
13.3.3 Scheduling 218 
References 221 
Index 233 
END
