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The Blind Passenger and the Assignment Problem

Published online by Cambridge University Press:  14 February 2011

JOHAN WÄSTLUND
JOHAN WÄSTLUND*
Affiliation:
Department of Mathematical Sciences, Chalmers University of Technology, S-412 96 Gothenburg, Sweden (e-mail: wastlund@chalmers.se)
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Abstract

We introduce a discrete random process which we call the passenger model, and show that it is connected to a certain random model of the assignment problem and in particular to the so-called Buck–Chan–Robbins urn process. We propose a conjecture on the distribution of the location of the minimum cost assignment in a cost matrix with zeros at specified positions and remaining entries of exponential distribution. The conjecture is consistent with earlier results on the participation probability of an individual matrix entry. We also use the passenger model to verify a conjecture by V. Dotsenko on the assignment problem.

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Type
Paper
Information
Combinatorics, Probability and Computing , Volume 20 , Issue 3 , May 2011 , pp. 467 - 480
Copyright
Copyright © Cambridge University Press 2011

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