On the hardness of approximating minimization problems
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Maximum matchings in sparse random graphs: Karp-Sipser revisited
Random Structures & Algorithms
Maximum matching in sparse random graphs
SFCS '81 Proceedings of the 22nd Annual Symposium on Foundations of Computer Science
A distributed greedy algorithm for connected sensor cover in dense sensor networks
DCOSS'05 Proceedings of the First IEEE international conference on Distributed Computing in Sensor Systems
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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 on-line 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: for d = c · n (c is a constant), the greedy and random algorithms are asymptotically equivalent; for fixed d, the greedy algorithms are asymptotically superior to the random algorithm; for graphs with d ≤ 3, the approximation ratio of the modified greedy algorithm is asymptotically We also consider random 3-regular graphs, for which non-trivial lower and upper bounds on the size of a maximum independent set are known. Our experiments suggest that the lower bound is asymptotically tight.