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

Abstract

The classical greedy heuristic for approximating maximum indepen- dent 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 natu- ral 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.