Khaled Ghedira is Professor at the University of Tunis, Tunisia.

Introduction xi

Chapter 1. Foundations of CSP 1

1.1. Basic concepts 1

1.2. CSP framework 3

1.2.1. Formalism 4

1.2.2. Areas of application 6

1.2.3. Extensions 17

1.3. Bibliography 22

Chapter 2. Consistency Reinforcement Techniques 29

2.1. Basic notions 29

2.1.1. Equivalence 29

2.1.2. K-consistency 30

2.2. Arc consistency reinforcement algorithms 32

2.2.1. AC-1 33

2.2.2. AC-2 36

2.2.3. AC-3 38

2.2.4. AC-4 41

2.2.5. AC-5 44

2.2.6. AC-6 50

2.2.7. AC-7 54

2.2.8. AC2000 61

2.2.9. AC2001 65

2.3. Bibliography 69

Chapter 3. CSP Solving Algorithms 73

3.1. Complete resolution methods 73

3.1.1. The backtracking algorithm 74

3.1.2. Look-back algorithms 76

3.1.3. Look-ahead algorithms 86

3.2. Experimental validation 92

3.2.1. Random generation of problems 92

3.2.2. Phase transition 94

3.3. Bibliography 96

Chapter 4. Search Heuristics 99

4.1. Organization of the search space 99

4.1.1. Parallel approaches 99

4.1.2. Distributed approaches 100

4.1.3. Collaborative approaches 102

4.2. Ordering heuristics 102

4.2.1. Illustrative example 102

4.2.2. Variable ordering 109

4.2.3. Value ordering 115

4.2.4. Constraints-based ordering 116

4.3. Bibliography 117

Chapter 5. Learning Techniques 121

5.1. The “nogood” concept 122

5.1.1. Example of union and projection 123

5.1.2. Use of nogoods 125

5.1.3. Nogood handling 125

5.2. Nogood-recording algorithm 126

5.3. The nogood-recording-forward-checking algorithm 129

5.4. The weak-commitment-nogood-recording algorithm 132

5.5. Bibliography 133

Chapter 6. Maximal Constraint Satisfaction Problems 135

6.1. Branch and bound algorithm 136

6.2. Partial Forward-Checking algorithm 138

6.3. Weak-commitment search 142

6.4. GENET method 144

6.5. Distributed simulated annealing 146

6.6. Distributed and guided genetic algorithm 147

6.6.1. Basic principles 148

6.6.2. The multi-agent model 150

6.6.3. Genetic process 152

6.6.4. Extensions 158

6.7. Bibliography 162

Chapter 7. Constraint Satisfaction and Optimization Problems 165

7.1. Formalism 166

7.2. Resolution methods 166

7.2.1. Branch-and-bound algorithm 167

7.2.2. Tunneling algorithm 170

7.3. Bibliography 178

Chapter 8. Distributed Constraint Satisfaction Problems 181

8.1. DisCSP framework 183

8.1.1. Formalism 183

8.1.2. Distribution modes 185

8.1.3. Communication models 191

8.1.4. Convergence properties 193

8.2. Distributed consistency reinforcement 195

8.2.1. The DisAC-4 algorithm 196

8.2.2. The DisAC-6 algorithm 197

8.2.3. The DisAC-9 algorithm 198

8.2.4. The DRAC algorithm 199

8.3. Distributed resolution 200

8.3.1. Asynchronous backtracking algorithm 201

8.3.2. Asynchronous weak-commitment search 204

8.3.3. Asynchronous aggregation search 205

8.3.4. Approaches based on canonical distribution 207

8.3.5. DOC approach 208

8.3.6. Generalization of DisCSP algorithms to several variables 214

8.4. Bibliography 215

Index 221

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