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Approximating the Sparsest k-Subgraph in Chordal Graphs

  • Rémi Watrigant
  • Marin Bougeret
  • Rodolphe Giroudeau
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8447)

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 \(\mathcal{NP}\)-hard and even not approximable unless \(\mathcal{P} = \mathcal{NP}\) 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 \(\mathcal{NP}\)-hardness of Sparsest k -Subgraph on chordal graphs, and a greedy 2-approximation algorithm. Finally, we also show how to derive a PTAS for Sparsest k -Subgraph on proper interval graphs.

Keywords

Interval Graph Chordal Graph Graph Class Perfect Graph Split Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

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

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