Finding Large Independent Sets in Polynomial Expected Time

We consider instances of the maximum independent set problem that are constructed according to the following semirandom model. Let Gn,p be a random graph, and let S be a set consisting of k vertices, chosen uniformly at random. Then, let G0 be the graph obtained by deleting all edges connecting two vertices in S. Finally, an adversary may add edges to G0 that do not connect two vertices in S, thereby producing the instance G = G n,p,k. We present an algorithm that in the case k C(n/p)1/2 , where C denotes a constant, on input G = G n,p,k finds an independent set of size k within polynomial expected time. Moreover, we prove that in the case k (1 - ) ln(n)/p this problem is hard.

• Type: Journal
• Year: 2006
• Where: CPC
• Authors: Amin Coja-Oghlan
• Keywords: Algorithm, CPC 2006, Input, Random Graph