## Greed is Good: Approximating Independent Sets in Sparse and . . . (1994)

Citations: | 55 - 7 self |

### BibTeX

@MISC{Halldorsson94greedis,

author = {Magnus M. Halldorsson and et al.},

title = {Greed is Good: Approximating Independent Sets in Sparse and . . . },

year = {1994}

}

### OpenURL

### Abstract

... for short, is one of the ~implest, most efficient, and most thoroughly studied methods for finding independent sets in graphs. We show that it surprisingly achieves a performance ratio of (A+ 2)/3 for approximating inde-pendent sets in graphs with degree bounded by A. The analysis directs us towards a simple parallel and dis-tributed algorithm with identical performance, which on constant-degree graphs runs in O(log ” n) time us-ing linear number of processors. We also analyze the Greedy algorithm when run in combination with a frac-tional relaxation technique of Nemhauser and Trotter, and obtain an improved (2Z + 3)/5 performance ratio on graphs with average degree ~. Finally, we introduce a generally applicable technique for improving the approximation ratios of independent set algorithms, and illustrate it by improving the per-formance ratio of Greedy for large ∆.