The greedier the better: an efficient algorithm for approximating maximum independent set

Authors:
H. Y. Lau;H. F. Ting
Affiliations:
Department of Computer Science and Information Systems, The University of Hong Kong, Hong Kong;Department of Computer Science and Information Systems, The University of Hong Kong, Hong Kong
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

The classical greedy heuristic for approximating maximum independent set is simple and efficient. It achieves a performance ratio bound of (Δ + 2)/3, where Δ is the degree of the input graph. All known algorithms for the problem with better ratio bounds are complicated and run slowly for moderately large Δ. In this paper, we describe a natural extension of the greedy heuristic. It is as simple and as efficient as the classical greedy heuristic. By a careful analysis on the structure of the intermediate graphs manipulated by our heuristic, we prove that the ratio bound is improved to (Δ + 3)/3.25.