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Theory of Computing Systems

, Volume 58, Issue 1, pp 111–132 | Cite as

Approximating the Sparsest k-Subgraph in Chordal Graphs

  • Rémi Watrigant
  • Marin Bougeret
  • Rodolphe Giroudeau
Article
  • 37k Downloads

Abstract

Given a simple undirected graph G = (V, E) and an integer k < |V|, the Sparsest k-Subgraph problem asks for a set of k vertices which induces the minimum number of edges. As a generalization of the classical independent set problem, Sparsest k-Subgraph is 𝓝𝓟-hard and even not approximable unless 𝓟𝓝𝓟 in general graphs. Thus, we investigate Sparsest k-Subgraph in graph classes where independent set is polynomial-time solvable, such as subclasses of perfect graphs. Our two main results are the 𝓝𝓟-hardness of Sparsest k-Subgraph on chordal graphs, and a greedy 2-approximation algorithm. Finally, we also show how to derive a P T A S for Sparsest k-Subgraph on proper interval graphs.

Keywords

Sparsest k-subgraph Approximation algorithm Chordal graphs 

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Rémi Watrigant
    • 1
  • Marin Bougeret
    • 1
  • Rodolphe Giroudeau
    • 1
  1. 1.LIRMMUniversité Montpellier 2Montpellier Cedex 5France

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