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 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 on input G = G ∗ n,p,k ﬁnds an independent set of size ≥ k within polynomial expected time, provided that k ≥ C(n/p)1/2 for a certain constant C > 0. Moreover, we prove that in the case k ≤ (1 − ε) ln(n)/p this problem is hard.
|Referee:||Hans Jürgen Prömel|
|Date of first Publication:||11.05.2005|
|Institute:||Humboldt-Universität zu Berlin|
|Project:||A5 Analysis and modelling of complex networks|
|Preprint Number:||Matheon Preprint #278|