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Average Case Analysis of a Heuristic for the Assignment Problem

Richard M. Karp, Alexander H. G. Rinnooy Kan and Rakesh V. Vohra
Mathematics of Operations Research
Vol. 19, No. 3 (Aug., 1994), pp. 513-522
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/3690326
Page Count: 10
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Average Case Analysis of a Heuristic for the Assignment Problem
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Abstract

Our main contribution is an O(n log n) algorithm that determines with high probability a perfect matching in a random 2-out bipartite graph. We also show that this algorithm runs in O(n) expected time. This algorithm can be used as a subroutine in an O(n2) heuristic for the assignment problem. When the weights in the assignment problem are independently and uniformly distributed in the interval [0, 1], we prove that the expected weight of the assignment returned by this heuristic is bounded above by $3+O(n^{-a})$, for some positive constant a.

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