Exact and Approximation Algorithms for Densest k-Subgraph

(Extended Abstract)
  • Nicolas Bourgeois
  • Aristotelis Giannakos
  • Giorgio Lucarelli
  • Ioannis Milis
  • Vangelis Th. Paschos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7748)

Abstract

The DENSEST k-SUBGRAPH problem is a generalization of the maximum clique problem, in which we are given a graph G and a positive integer k, and we search among the subsets of k vertices of G one inducing a maximum number of edges. In this paper, we present algorithms for finding exact solutions of k-SUBGRAPH improving the trivial exponential time complexity of O*(2n) and using polynomial space. Two FPT algorithms are also proposed; the first considers as parameter the treewidth of the input graph and uses exponential space, while the second is parameterized by the size of the minimum vertex cover and uses polynomial space. Finally, we propose several approximation algorithms running in moderately exponential or parameterized time.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Nicolas Bourgeois
    • 1
  • Aristotelis Giannakos
    • 2
  • Giorgio Lucarelli
    • 3
  • Ioannis Milis
    • 4
  • Vangelis Th. Paschos
    • 2
    • 5
  1. 1.ESSECFrance
  2. 2.PSL Research University, Université Paris-Dauphine, LAMSADE, CNRS UMRParisFrance
  3. 3.Université Pierre et Marie Curie, LIP6ParisFrance
  4. 4.Dept. of InformaticsAthens University of Economics and BusinessAthensGreece
  5. 5.Institut Universitaire de FranceFrance

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