Approximation algorithms for dispersion problems
Journal of Algorithms
Greedy facility location algorithms analyzed using dual fitting with factor-revealing LP
Journal of the ACM (JACM)
AdWords and Generalized On-line Matching
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Approximation algorithms for maximum dispersion
Operations Research Letters
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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Given a positive integer p and a complete graph with non-negative edge weights that satisfy the triangle inequality, the remote-clique problem is to find a subset of p 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 present an algorithm called d-Greedy Augment that generalizes this greedy algorithm (they are equivalent when d = 1). We use the technique of factor-revealing linear programs to prove that d-Greedy Augment, which has a running time of O(pdnd), achieves an approximation ratio of (2p – 2)/(p + d – 2). Thus, when d = 1, d-Greedy Augment achieves an approximation ratio of 2 and runs in time O(pn), making it the fastest known 2-approximation for the remote-clique problem. The usefulness of factor-revealing LPs in the analysis of d-Greedy Augment suggests possible applicability of this technique to the study of other approximation algorithms.