We consider the problem of finding a maximum independent set in a random graph. The random graph G is modelled as follows. Every edge is included independently with probability \(\frac{d}{n}\), where d is some sufficiently large constant. Thereafter, for some constant α, a subset I of αn vertices is chosen at random, and all edges within this subset are removed. In this model, the planted independent set I is a good approximation for the maximum independent set I max , but both II max and I max I are likely to be nonempty. We present a polynomial time algorithms that with high probability (over the random choice of random graph G, and without being given the planted independent set I) finds a maximum independent set in G when \(\alpha \geq \sqrt{c_0 \log d /d}\), where c 0 is some sufficiently large constant independent of d.


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Uriel Feige
    • 1
  • Eran Ofek
    • 1
  1. 1.Department of Computer Science and Applied MathematicsWeizmann Institute of ScienceRehovotIsrael

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