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2009 50th Annual IEEE Symposium on Foundations of Computer Science (2009)
Atlanta, GA
Oct. 25, 2009 to Oct. 27, 2009
ISSN: 0272-5428
ISBN: 978-1-4244-5116-6
pp: 427-436
We study the prize-collecting versions of the Steiner tree, traveling salesman, and stroll (a.k.a. Path-TSP) problems (PCST, PCTSP, and PCS, respectively): given a graph (V, E) with costs on each edge and a penalty (a.k.a. prize) on each node, the goal is to find a tree (for PCST), cycle (for PCTSP), or stroll (for PCS) that minimizes the sum of the edge costs in the tree/cycle/stroll and the penalties of the nodes not spanned by it. In addition to being a useful theoretical tool for helping to solve other optimization problems, PCST has been applied fruitfully by AT&T to the optimization of real-world telecommunications networks. The most recent improvements for the first two problems, giving a 2-approximation algorithm for each, appeared first in 1992. (A 2-approximation for PCS appeared in 2003.) The natural linear programming (LP) relaxation of PCST has an integrality gap of 2, which has been a barrier to further improvements for this problem. We present (2 · ¿)-approximation algorithms for all three problems, connected by a unified technique for improving prize-collecting algorithms that allows us to circumvent the integrality gap barrier.
approximation theory, linear programming, relaxation theory, travelling salesman problems, trees (mathematics)

A. Archer, M. H. Bateni, M. T. Hajiaghayi and H. Karloff, "Improved Approximation Algorithms for PRIZE-COLLECTING STEINER TREE and TSP," 2009 50th Annual IEEE Symposium on Foundations of Computer Science(FOCS), Atlanta, Georgia, 2010, pp. 427-436.
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