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Maximum Independent Set in Graphs of Average Degree at Most Three in \({\mathcal O}(1.08537^n)\)

  • Nicolas Bourgeois
  • Bruno Escoffier
  • Vangelis Th. Paschos
  • Johan M. M. van Rooij
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6108)

Abstract

We show that Maximum Independent Set on connected graphs of average degree at most three can be solved in \({\mathcal O}(1.08537^n)\) time and linear space. This improves previous results on graphs of maximum degree three, as our connectivity requirement only functions to ensure that each connected component has average degree at most three.

We link this result to exact algorithms of Maximum Independent Set on general graphs. Also, we obtain a faster parameterised algorithm for Vertex Cover restricted to graphs of maximum degree three running in time \({\mathcal O}^*(1.1781^k)\).

Keywords

Maximum Degree Average Degree Vertex Cover General Graph Reduction Rule 
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-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Nicolas Bourgeois
    • 1
  • Bruno Escoffier
    • 1
  • Vangelis Th. Paschos
    • 1
  • Johan M. M. van Rooij
    • 2
  1. 1.LAMSADECNRS FRE 3234 and Université Paris-DauphineFrance
  2. 2.Department of Information and Computing SciencesUtrecht UniversityUtrechtThe Netherlands

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