... for short, is one of the simplest, 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 independent sets in graphs with degree bounded by A. The analysis directs us towards a simple parallel and distributed algorithm with identical performance, which on constant-degree graphs runs in O(log* n) time using linear number of processors. We also analyze the Greedy algorithm when run in combination with a fractional 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 performance ratio of Greedy for large ∆
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