Necessary Condition for Path Partitioning Constraints

Authors:
Nicolas Beldiceanu;Xavier Lorca
Affiliations:
École des Mines de Nantes, LINA FRE CNRS 2729, FR --- 44307 Nantes Cedex 3,;École des Mines de Nantes, LINA FRE CNRS 2729, FR --- 44307 Nantes Cedex 3,
Venue:
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2007

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Abstract

Given a directed graph $\mathcal{G}$, the Knode-disjoint paths problem consists in finding a partition of $\mathcal{G}$ into Knode-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 Knode-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.