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APPROX

2009

Springer

2009

Springer

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-speciﬁc 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 sparsiﬁed graph is within some multiplicative factor and/or additive constant of the original distance has received substantial study in theoreti...

Added |
25 May 2010 |

Updated |
25 May 2010 |

Type |
Conference |

Year |
2009 |

Where |
APPROX |

Authors |
Prasad Chebolu, Alan M. Frieze, Páll Melsted, Gregory B. Sorkin |

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