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Average-case analyses of Vickrey costs

Chebolu, Prasad , Frieze, Alan , Melsted, Páll and Sorkin, Gregory B. (2009) Average-case analyses of Vickrey costs. In: Dinur, Irit , Jansen, Klaus , Naor, Seffi and Rolim, José , (eds.) Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques:12th International Workshop, Approx 2009. Lecture notes in computer science(5687). Springer, pp. 434-447. ISBN 9783642036842

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Abstract

We explore the average-case "Vickrey" cost of structures in a random setting: the Vickrey cost of a shortest path in a complete graph or digraph with random edge weights; the Vickrey cost of a minimum spanning tree (MST) in a complete graph with random edge weights; and the Vickrey cost of a perfect matching in a complete bipartite graph with random edge weights. In each case, in the large-size limit, the Vickrey cost is precisely 2 times the (non-Vickrey) minimum cost, but this is the result of case-specic calculations, with no general reason found for it to be true. Separately, we consider the problem of sparsifying a complete graph with random edge weights so that all-pairs shortest paths are preserved approximately. The problem of sparsifying a given graph so that for every pair of vertices, the length of the shortest path in the sparsied graph is within some multiplicative factor and/or additive constant of the original distance has received substantial study in theoretical computer science. For the complete graph Kn with additive edge weights, we show that whp ( n lnn) edges are necessary and sucient for a spanning subgraph to give good all-pairs shortest paths approximations.

Item Type: Book Section
Official URL: http://www.springer.com
Additional Information: © 2009 Springer
Library of Congress subject classification: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Sets: Research centres and groups > Management Science Group
Departments > Management
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 13 May 2011 10:36
URL: http://eprints.lse.ac.uk/35634/

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