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"Microsoft Research Audio 105103: Improved Approximation Algorithms For Prize-Collecting Steiner Tree And TSP" and the language of the book is English.


“Microsoft Research Audio 105103: Improved Approximation Algorithms For Prize-Collecting Steiner Tree And TSP” Metadata:

  • Title: ➤  Microsoft Research Audio 105103: Improved Approximation Algorithms For Prize-Collecting Steiner Tree And TSP
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  • Language: English

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  • Internet Archive ID: ➤  Microsoft_Research_Audio_105103

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<p>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.</p><p>We present (2 - epsilon)-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.</p><div class="fs30">©2009 Microsoft Corporation. All rights reserved.</div>

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