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

Walid Ben-Ameur (), Mohamed-Ahmed Mohamed-Sidi () and José Neto ()
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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

Journal of Combinatorial Optimization, 2015, vol. 29, issue 1, No 18, 276-307

Abstract: 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.

Keywords: Graph partitioning; Complexity theory; Optimization; Approximation algorithms; Polyhedra (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10878-014-9753-x

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