Chapter

Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems

Volume 4510 of the series Lecture Notes in Computer Science pp 141-154

Necessary Condition for Path Partitioning Constraints

  • Nicolas BeldiceanuAffiliated withÉcole des Mines de Nantes, LINA FRE CNRS 2729, FR – 44307 Nantes Cedex 3
  • , Xavier LorcaAffiliated withÉcole des Mines de Nantes, LINA FRE CNRS 2729, FR – 44307 Nantes Cedex 3

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Abstract

Given a directed graph \(\mathcal{G}\), the K node-disjoint paths problem consists in finding a partition of \(\mathcal{G}\) into K node-disjoint paths, such that each path ends up in a given subset of nodes in \(\mathcal{G}\). This article provides a necessary condition for the K node-disjoint paths problem which combines (1) the structure of the reduced graph associated with \(\mathcal{G}\), (2) the structure of each strongly connected component of \(\mathcal{G}\) with respect to dominance relation between nodes, and (3) the way the nodes of two strongly connected components are inter-connected. This necessary condition is next used to deal with a path partitioning constraint.