A novel parameterised approximation algorithm for minimum vertex cover

  • Authors:

  • Ljiljana Brankovic;Henning Fernau

  • Affiliations:

  • School of Electrical Engineering and Computer Science, The University of Newcastle, Callaghan, NSW 2308, Australia;Fachbereich 4, Abteilung Informatik, Universität Trier, D-54286 Trier, Germany

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2013

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Abstract

Parameterised approximation is a relatively new but growing field of interest. It merges two ways of dealing with NP-hard optimisation problems, namely polynomial approximation and exact parameterised (exponential-time) algorithms. We exemplify this idea by designing and analysing parameterised approximation algorithms for minimum vertex cover. More specifically, we provide a simple algorithm that works on any approximation ratio of the form 2l+1l+1, l=1,2,..., and has complexity that outperforms previously published algorithms based on sophisticated exact parameterised algorithms. In particular, for l=1 (factor-1.5 approximation) our algorithm runs in time O^*(1.0883^k), where parameter k@?23@t, and @t is the size of a minimum vertex cover. Additionally, we present an improved polynomial-time approximation algorithm for graphs of average degree at most four and a limited number of vertices with degree less than two.