The max quasi-independent set Problem

  • N. Bourgeois
  • A. Giannakos
  • G. Lucarelli
  • I. Milis
  • V. Th. Paschos
  • O. Pottié
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6072)

Abstract

In this paper, we deal with the problem of finding quasi-independent sets in graphs. This problem is formally defined in three versions, which are shown to be polynomially equivalent. The one that looks most general, namely, f-QIS, consists of, given a graph and a non-decreasing function f, finding a maximum size subset Q of the vertices of the graph, such that the number of edges in the induced subgraph is less than or equal to f(|Q|). For this problem, we show an exact solution method that runs within time \(O^*(2^{\frac{d-27/23}{d+1}n})\) on graphs of average degree bounded by d. For the most specifically defined γ-QIS and k-QIS problems, several results on complexity and approximation are shown, and greedy algorithms are proposed, analyzed and tested.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • N. Bourgeois
    • 1
  • A. Giannakos
    • 1
  • G. Lucarelli
    • 1
    • 2
  • I. Milis
    • 2
  • V. Th. Paschos
    • 1
  • O. Pottié
    • 1
  1. 1.LAMSADECNRS and Université Paris-DauphineFrance
  2. 2.Department of InformaticsAthens University of Economics and BusinessGreece

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