Experimental Evaluation of the Greedy and Random Algorithms for Finding Independent Sets in Random Graphs

This work is motivated by the long-standing open problem of designing a polynomial-time algorithm that with high probability constructs an asymptotically maximum independent set in a random graph. We present the results of an experimental investigation of the comparative performance of several efficient heuristics for constructing maximal independent sets. Among the algorithms that we evaluate are the well known randomized heuristic, the greedy heuristic, and a modification of the latter which breaks ties in a novel way. All algorithms deliver online upper bounds on the size of the maximum independent set for the specific input-graph. In our experiments, we consider random graphs parameterized by the number of vertices n and the average vertex degree d. Our results provide strong experimental evidence in support of the following conjectures:

• Type: Conference
• Year: 2005
• Where: WEA
• Authors: Mark K. Goldberg, D. Hollinger, Malik Magdon-Ismail
• Keywords: Algorithms, Independent Set, Maximum Independent Set, Random Graphs, WEA 2005