Constructive bounds and exact expectation for the random assignment problem
Random Structures & Algorithms
The ζ (2) limit in the random assignment problem
Random Structures & Algorithms
On the expected value of the minimum assignment
Random Structures & Algorithms
Exact Expectations and Distributions for the Random Assignment Problem
Combinatorics, Probability and Computing
On Random Symmetric Travelling Salesman Problems
Mathematics of Operations Research
A proof of a conjecture of Buck, Chan, and Robbins on the expected value of the minimum assignment
Random Structures & Algorithms - Proceedings of the Eleventh International Conference "Random Structures and Algorithms," August 9—13, 2003, Poznan, Poland
Proofs of the Parisi and Coppersmith-Sorkin random assignment conjectures
Random Structures & Algorithms
Size and Weight of Shortest Path Trees with Exponential Link Weights
Combinatorics, Probability and Computing
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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.