, Volume 18, Issue 1, pp 145-163

Greed is good: Approximating independent sets in sparse and bounded-degree graphs

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Abstract

Theminimum-degree greedy algorithm, or Greedy for short, is a simple and well-studied method for finding independent sets in graphs. We show that it achieves a performance ratio of (Δ+2)/3 for approximating independent sets in graphs with degree bounded by Δ. The analysis yields a precise characterization of the size of the independent sets found by the algorithm as a function of the independence number, as well as a generalization of Turán’s bound. We also analyze the algorithm when run in combination with a known preprocessing technique, and obtain an improved \((2\bar d + 3)/5\) performance ratio on graphs with average degree \(\bar d\) , improving on the previous best \((\bar d + 1)/2\) of Hochbaum. Finally, we present an efficient parallel and distributed algorithm attaining the performance guarantees of Greedy.

Gordon Gekko [29].
A preliminary version of this paper appeared at the 26th ACM Symposium on Theory of Computing, 1994. This work was done while both authors were at the Japan Advanced Institute of Science and Technology, Hokuriku.
Communicated by M. X. Goemans.