An Improved Analysis for a Greedy Remote-Clique Algorithm Using Factor-Revealing LPs

Given a positive integer k and a complete graph with non-negative edge weights satisfying the triangle inequality, the remote-clique problem is to find a subset of k vertices having a maximum-weight induced subgraph. A greedy algorithm for the problem has been shown to have an approximation ratio of 4, but this analysis was not shown to be tight. In this paper, we use the technique of factor-revealing linear programs to show that the greedy algorithm actually achieves an approximation ratio of 2, which is tight. This research was supported in part by the National Science Foundation under grant CISE-EI-0305954 and was performed while the first author was at Washington University in St. Louis. A preliminary version of this paper appears in RANDOM-APPROX ’06, volume 4110 of Lecture Notes in Computer Science, pp. 49–60, 2006.