ON THE RANDOM n×n ASSIGNMENT PROBLEM

Title & Authors
ON THE RANDOM n×n ASSIGNMENT PROBLEM
Lee, Sung-Chul; Zhonggen, Su;

Abstract
Consider the random n $\small{\times}$ m assignment problem with m $\small{\geq}$ $\small{_{i,j}}$ Let $\small{u_{i,j}}$ be iid uniform random variables on [0, 1] and exponential random variables with mean 1, respectively, and let $\small{U_{n, m}}$ and $\small{T_{n, m}}$ denote the optimal assignment costs corresponding to $\small{u_{i, j}}$ and $\small{t_{i, j}}$. In this paper we first give a comparison result about the discrepancy E $\small{T_{n, m}}$ -E $\small{U_{n, m}}$. Using this comparison result with a known lower bound for Var( $\small{T_{n, m}}$) we obtains a lower bound for Var( $\small{U_{n, m}}$). Finally, we study the way that E $\small{U_{n, m}}$ and E $\small{T_{n, m}}$ vary as m does. It turns out that only when m - n is large enough, the cost decreases significantly.tly.
Keywords
n$\small{{\times}}$m assignment problem;bipartite matching;optimal assignment;
Language
English
Cited by
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