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

Authors:
Benjamin Birnbaum;Kenneth J. Goldman
Affiliations:
University of Washington, Department of Computer Science and Engineering, Box 352350, 98105-2350, Seattle, WA, USA;Washington University in St. Louis, Department of Computer Science and Engineering, Campus Box 1045, One Brookings Drive, 63130-4899, St. Louis, MO, USA
Venue:
Algorithmica
Year:
2009

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Abstract

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.