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Necessary Condition for Path Partitioning Constraints

  • Conference paper
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4510))

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.

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Authors and Affiliations

  1. École des Mines de Nantes, LINA FRE CNRS 2729, FR – 44307 Nantes Cedex 3,  

    Nicolas Beldiceanu & Xavier Lorca

Authors
  1. Nicolas Beldiceanu
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  2. Xavier Lorca
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Pascal Van Hentenryck Laurence Wolsey

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Beldiceanu, N., Lorca, X. (2007). Necessary Condition for Path Partitioning Constraints. In: Van Hentenryck, P., Wolsey, L. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2007. Lecture Notes in Computer Science, vol 4510. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72397-4_11

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  • DOI: https://doi.org/10.1007/978-3-540-72397-4_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72396-7

  • Online ISBN: 978-3-540-72397-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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