The Blind Passenger and the Assignment Problem

• 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.

Ämnesord

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Nyckelord

traveling salesman

minimum assignment

expected value

zeta(2) limit

proof

conjecture

expected value

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