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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Lorca, Xavier. Tree-based Graph Partitioning Constraint. London : Wiley, ©2013 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Xavier Lorca |

OCLC Number: | 827208456 |

Notes: | 6.5. Relation of conditional precedence. |

Description: | 1 online resource (252 pages). |

Contents: | Cover; Tree-based Graph Partitioning Constraint; Title Page; Copyright Page; Table of Contents; PART 1. CONSTRAINT PROGRAMMING AND FOUNDATIONS OF GRAPH THEORY; Introduction to Part 1; Chapter 1. Introduction to Constraint Programming; 1.1. What is a variable?; 1.2. What is a constraint?; 1.3. What is a global constraint?; 1.4. What is a propagation algorithm?; 1.5. What is a consistency level?; 1.6. What is a constraint solver?; 1.7. Constraint solvers at work; 1.7.1. Importance of modeling; 1.7.2. Importance of heuristics in guiding research; 1.7.3. Importance of using global constraints. 1.8. Organization structureChapter 2. Graph Theory and Constraint Programming; 2.1. Modeling graphs with constraint programming; 2.1.1. Representing a family of graphs; 2.1.2. Useful graph definitions and properties; 2.1.3. Graph implementation and complexity; 2.2. Graph theory at work in constraint programming; 2.3. Constraint programming at work in graph theory; Chapter 3. Tree Graph Partitioning; 3.1. In undirected graphs; 3.2. In directed graphs; PART 2. CHARACTERIZATION OF TREE-BASED GRAPH PARTITIONING CONSTRAINTS; Chapter 4. Tree Constraints in UndirectedGraphs; 4.1. Decomposition. 4.2. Definition of constraints4.3. A filtering algorithm for the proper-forest constraint; 4.3.1. A solution for the proper-forest constraint; 4.3.2. Hybrid-consistency for the proper-forest constraint; 4.3.3. Correction and completion; 4.3.4. Complexity; 4.4. Filtering algorithm for the resource-forest constraint; 4.4.1. Existence of a solution for the resource-forest constraint; 4.4.2. Hybrid-consistency for the resource-forest constraint; 4.4.3. Correction and completion; 4.4.4. Complexity; 4.5. Summary of undirected tree constraints; Chapter 5. Tree Constraints in Directed Graphs. 5.1. Decomposition5.2. Definition of constraints; 5.3. Filtering algorithm for the tree constraint; 5.3.1. Existence of a solution for a tree constraint; 5.3.2. General arc-consistency for the tree constraint; 5.3.3. Correction and completion; 5.3.4. Complexity; 5.4. Filtering algorithm for the proper-tree constraint; 5.4.1. Limits on the number of proper trees; 5.4.2. Existence of a solution for the proper-tree constraint; 5.4.3. Filtering algorithm for the proper-tree constraint; 5.4.4. Correction; 5.4.5. Complexity; 5.5. Summary of tree constraints in directed and undirected graphs. Chapter 6. Additional Constraints Linked to Graph Partitioning6.1. Definition of restrictions; 6.2. Complexity zoo; 6.2.1. Proper trees; 6.2.2. Precedence constraints; 6.2.3. Conditional precedence constraints; 6.2.4. Constraints on the interior half-degree of vertices; 6.2.5. Incomparability constraints; 6.3. Interaction between the number of trees and the number of proper trees; 6.4. Relation of precedence between the vertices of the graph; 6.4.1. Limitations on the maximum number of trees; 6.4.2. Filtering linked to a set of precedence constraints; 6.4.3. Filtering and complexity algorithm. |

Series Title: | ISTE. |

### Abstract:

Combinatorial problems based on graph partitioning enable us to mathematically represent and model many practical applications. Mission planning and the routing problems occurring in logistics perfectly illustrate two such examples. Nevertheless, these problems 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 theoretical problems like the Hamiltonian path problem, or K-node disjoint path problems. Indeed, they usually combine the graph partitioning problem with sever.

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