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The $$k$$ k -separator problem: polyhedra, complexity and approximation results

Author

Listed:
  • Walid Ben-Ameur

    (Télécom SudParis, CNRS Samovar UMR 5157)

  • Mohamed-Ahmed Mohamed-Sidi

    (Télécom SudParis, CNRS Samovar UMR 5157)

  • José Neto

    (Télécom SudParis, CNRS Samovar UMR 5157)

Abstract

Given a vertex-weighted undirected graph $$G=(V,E,w)$$ G = ( V , E , w ) and a positive integer $$k$$ k , we consider the $$k$$ k -separator problem: it consists in finding a minimum-weight subset of vertices whose removal leads to a graph where the size of each connected component is less than or equal to $$k$$ k . We show that this problem can be solved in polynomial time for some graph classes including bounded treewidth, $$m K_2$$ m K 2 -free, $$(G_1, G_2, G_3, P_6)$$ ( G 1 , G 2 , G 3 , P 6 ) -free, interval-filament, asteroidal triple-free, weakly chordal, interval and circular-arc graphs. Polyhedral results with respect to the convex hull of the incidence vectors of $$k$$ k -separators are reported. Approximation algorithms are also presented.

Suggested Citation

  • Walid Ben-Ameur & Mohamed-Ahmed Mohamed-Sidi & José Neto, 2015. "The $$k$$ k -separator problem: polyhedra, complexity and approximation results," Journal of Combinatorial Optimization, Springer, vol. 29(1), pages 276-307, January.
    • Handle: RePEc:spr:jcomop:v:29:y:2015:i:1:d:10.1007_s10878-014-9753-x
    DOI: 10.1007/s10878-014-9753-x
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    References listed on IDEAS

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    1. Maarten Oosten & Jeroen H. G. C. Rutten & Frits C. R. Spieksma, 2007. "Disconnecting graphs by removing vertices: a polyhedral approach," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 61(1), pages 35-60, February.
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    Cited by:

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