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Greed is good: Approximating independent sets in sparse and bounded-degree graphs. (English) Zbl 0866.68077
Summary: 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 $$(\Delta+2)/3$$ for approximating independent sets in graphs with degree bounded by $$\Delta$$. 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 $$(2\overline d+3)/5$$ performance ratio on graphs with average degree $$\overline d$$, improving on the previous best $$(\overline d+1)/2$$ of Hochbaum. Finally, we present an efficient parallel and distributed algorithm attaining the performance guarantees of Greedy.

##### MSC:
 68R10 Graph theory (including graph drawing) in computer science 05C35 Extremal problems in graph theory
##### Keywords:
minimum-degree greedy algorithm
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##### References:
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