Approximating independent set in perturbed graphs

Authors:
Bodo Manthey;Kai Plociennik
Affiliations:
University of Twente, Department of Applied Mathematics, P. O. Box 217, 7500 AE Enschede, The Netherlands;Fraunhofer Institute for Industrial Mathematics ITWM, Department "Optimization", Fraunhofer-Platz 1, 67663 Kaiserslautern, Germany
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

For the maximum independent set problem, strong inapproximability bounds for worst-case efficient algorithms exist. We give a deterministic algorithm beating these bounds, with polynomial expected running-time for semi-random graphs: an adversary chooses a graph with n vertices, and then edges are flipped with a probability of @e. Our algorithm guarantees an approximation ratio of O(n@e) for sufficiently large @e.