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Minimum d-blockers and d-transversals in graphs

Author

Listed:
  • Marie-Christine Costa

    (Ecole Nationale Supérieure des Techniques Avancées-Paristech and CEDRIC Laboratory)

  • Dominique Werra

    (Ecole Polytechnique Fédérale de Lausanne)

  • Christophe Picouleau

    (Conservatoire National des Arts et Métiers, CEDRIC Laboratory)

Abstract

We consider a set V of elements and an optimization problem on V: the search for a maximum (or minimum) cardinality subset of V verifying a given property ℘. A d-transversal is a subset of V which intersects any optimum solution in at least d elements while a d-blocker is a subset of V whose removal deteriorates the value of an optimum solution by at least d. We present some general characteristics of these problems, we review some situations which have been studied (matchings, s–t paths and s–t cuts in graphs) and we study d-transversals and d-blockers of stable sets or vertex covers in bipartite and in split graphs.

Suggested Citation

  • Marie-Christine Costa & Dominique Werra & Christophe Picouleau, 2011. "Minimum d-blockers and d-transversals in graphs," Journal of Combinatorial Optimization, Springer, vol. 22(4), pages 857-872, November.
    • Handle: RePEc:spr:jcomop:v:22:y:2011:i:4:d:10.1007_s10878-010-9334-6
    DOI: 10.1007/s10878-010-9334-6
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    References listed on IDEAS

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    1. Olivier Goldschmidt & Dorit S. Hochbaum, 1994. "A Polynomial Algorithm for the k-cut Problem for Fixed k," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 24-37, February.
    2. Benoît Colson & Patrice Marcotte & Gilles Savard, 2007. "An overview of bilevel optimization," Annals of Operations Research, Springer, vol. 153(1), pages 235-256, September.
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