Lorca Tree-based Graph Partitioning Constraint

1. Auflage 2013
ISBN: 978-1-118-60360-4
Verlag: John Wiley & Sons
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 240 Seiten, E-Book

Combinatorial problems based on graph partitioning enable us tomathematically represent and model many practical applications.Mission planning and the routing problems occurring in logisticsperfectly illustrate two such examples. Nevertheless, theseproblems are not based on the same partitioning pattern: generally,patterns like cycles, paths, or trees are distinguished. Moreover,the practical applications are often not limited to theoreticalproblems like the Hamiltonian path problem, or K-node disjoint pathproblems. Indeed, they usually combine the graph partitioningproblem with several restrictions related to the topology of nodesand arcs. The diversity of implied constraints in real-lifeapplications is a practical limit to the resolution of suchproblems by approaches considering the partitioning problemindependently from each additional restriction.
This book focuses on constraint satisfaction problems related totree partitioning problems enriched by several additionalconstraints that restrict the possible partitions topology. On theone hand, this title focuses on the structural properties of treepartitioning constraints. On the other hand, it is dedicated to theinteractions between the tree partitioning problem and classicalrestrictions (such as precedence relations or incomparabilityrelations between nodes) involved in practical applications.
Precisely, Tree-based Graph Partitioning Constraint shows how toglobally take into account several restrictions within one singletree partitioning constraint. Another interesting aspect of thisbook is related to the implementation of such a constraint. In thecontext of graph-based global constraints, the book illustrates howa fully dynamic management of data structures makes the runtime offiltering algorithms independent of the graph density.

Autoren/Hrsg.

Lorca, X.

Inhaltsverzeichnis

PART 1. CONSTRAINT PROGRAMMING AND FOUNDATIONS OF GRAPHTHEORY 1
Introduction to Part 1 3
Chapter 1. Introduction to Constraint Programming 5
1.1. What is a variable? 7
1.2. What is a constraint? 8
1.3. What is a global constraint? 10
1.4. What is a propagation algorithm? 11
1.5. What is a consistency level? 14
1.6. What is a constraint solver? 15
1.7. Constraint solvers at work 17
1.8. Organization structure 21
Chapter 2. Graph Theory and Constraint Programming 23
2.1. Modeling graphs with constraint programming 24
2.2. Graph theory at work in constraint programming 34
2.3. Constraint programming at work in graph theory 37
Chapter 3. Tree Graph Partitioning 39
3.1. In undirected graphs 39
3.2. In directed graphs 42
PART 2. CHARACTERIZATION OF TREE-BASED GRAPH PARTITIONINGCONSTRAINTS 47
Chapter 4. Tree Constraints in Undirected Graphs 49
4.1. Decomposition 49
4.2. Definition of constraints 51
4.3. A filtering algorithm for the proper-forest constraint56
4.4. Filtering algorithm for the resource-forest constraint70
4.5. Summary of undirected tree constraints 80
Chapter 5. Tree Constraints in Directed Graphs 83
5.1. Decomposition 83
5.2. Definition of constraints 86
5.3. Filtering algorithm for the tree constraint 89
5.4. Filtering algorithm for the proper-tree constraint 96
5.5. Summary of tree constraints in directed and undirectedgraphs 113
Chapter 6. Additional Constraints Linked to GraphPartitioning 117
6.1. Definition of restrictions 118
6.2. Complexity zoo 123
6.3. Interaction between the number of trees and the number ofproper trees 129
6.4. Relation of precedence between the vertices of the graph130
6.5. Relation of conditional precedence 137
6.6. Relation of incomparability between graph vertices 140
6.7. Interactions between precedence and incomparabilityconstraints 143
6.8. Constraining the interior half-degree of each vertex148
6.9. Summary 151
Chapter 7. The Case of Disjoint Paths 153
7.1. Minimum number of paths in acyclic directed graphs 156
7.2. Minimum number of paths in any directed graph 161
7.3. A path partitioning constraint 169
7.4. Summary 173
Chapter 8. Implementation of a Tree Constraint 175
8.1. Original implementation 176
8.2. Toward a "portable" implementation 181
8.3. Conclusion 191
PART 3. IMPLEMENTATION: TASK PLANNING 193
Introduction to Part 3 195
Chapter 9. First Model in Constraint Programming 199
9.1. Model for the coherence of displacements in space 199
9.2. Modeling resource consumption 200
9.3. Modeling time windows 201
9.4. Modeling coordination constraints between units 202
9.5. Limitations of the proposed model 203
Chapter 10. Advanced Model in Constraint Programming205
10.1. Modeling the coherence of displacements in space 206
10.2. Modeling resource consumption 208
10.3. Integration of temporal aspects 208
10.4. Propagating time windows 213
PART 4. CONCLUSION AND FUTURE WORK 225
Chapter 11. Conclusion 227
Chapter 12. Perspectives and Criticisms 231
Bibliography 233
Index 239