Finding a Maximum Independent Set in a Sparse Random Graph

We consider the problem of finding a maximum independent set in a random graph. The random graph G, which contains n vertices, is modelled as follows. Every edge is included independently with probability 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 Imax, but both I \Imax and Imax \ 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 the maximum independent set in G when α ≥ pc0 d , where c0 is some sufficiently large constant independent of d.

• Type: Conference
• Year: 2005
• Where: APPROX
• Authors: Uriel Feige, Eran Ofek
• Keywords: Algorithms, APPROX 2005, Independent Set, Maximum Independent Set, Random Graph