BIT Numerical Mathematics

, Volume 32, Issue 2, pp 180–196 | Cite as

Approximating maximum independent sets by excluding subgraphs

  • Ravi Boppana
  • Magnús M. Halldórsson
Algorithm Theory


An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known toO(n/(logn)2). We also obtain the same performance guarantee for graph coloring. The results can be combined into a surprisingly strongsimultaneous performance guarantee for the clique and coloring problems.

The framework ofsubgraph-excluding algorithms is presented. We survey the known approximation algorithms for the independent set (clique), coloring, and vertex cover problems and show how almost all fit into that framework. We show that among subgraph-excluding algorithms, the ones presented achieve the optimal asymptotic performance guarantees.

CR Categories

F.2.2 G.2.2 


Approximation algorithms independent sets graph coloring 


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Copyright information

© BIT Foundations 1992

Authors and Affiliations

  • Ravi Boppana
    • 1
    • 2
  • Magnús M. Halldórsson
    • 1
    • 2
  1. 1.Department of Computer ScienceNew York UniversityNew YorkUSA
  2. 2.School of Information ScienceJapan Advanced Institute of Science and Technology, HokurikuIshikawaJapan

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