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Reports Year : 2012

The k-Sparsest Subgraph Problem

Abstract

Given a simple undirected graph G = (V, E) and an integer k ≤ |V|, the k-sparsest subgraph problem asks for a set of k vertices that induce the minimum number of edges. As a generalization of the classical independent set problem, k-sparsest subgraph cannot ad- mit (unless P = NP) neither an approximation nor an FPT algorithm (parameterized by the number of edges in the solution) in all graph classes where independent set is NP-hard. Thus, it appears natural to investigate the approximability and fixed parameterized tractability of k-sparsest subgraph in graph classes where independent set is polynomial, such as subclasses of perfect graphs. In this paper, we first present a simple greedy tight 2-approximation algorithm in proper interval graphs, and then we use dynamic programming to design a PTAS in proper interval graph and an FPT algorithm in interval graphs (parameterized by the number of edges in the solution).
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Dates and versions

lirmm-00735713 , version 1 (26-09-2012)
lirmm-00735713 , version 2 (18-01-2013)

Identifiers

  • HAL Id : lirmm-00735713 , version 2

Cite

Rémi Watrigant, Marin Bougeret, Rodolphe Giroudeau. The k-Sparsest Subgraph Problem. RR-12019, 2012. ⟨lirmm-00735713v2⟩
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