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

- Received:
- Revised:

DOI: 10.1007/BF02523693

- Cite this article as:
- Halldórsson, M.M. & Radhakrishnan, J. Algorithmica (1997) 18: 145. doi:10.1007/BF02523693

- 63 Citations
- 795 Downloads

## Abstract

The*minimum-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.