Asymptotic behavior of the expected optimal value of the multidimensional assignment problem

Pavlo A. Krokhmal, Don A. Grundel, Panos M. Pardalos

Research output: Contribution to journalArticle

12 Scopus citations

Abstract

The Multidimensional Assignment Problem (MAP) is a higher-dimensional version of the Linear Assignment Problem that arises in the areas of data association, target tracking, resource allocation, etc. This paper elucidates the question of asymptotical behavior of the expected optimal value of the large-scale MAP whose assignment costs are independent identically distributed random variables with a prescribed probability distribution. We demonstrate that for a broad class of continuous distributions the limiting value of the expected optimal cost of the MAP is determined by the location of the left endpoint of the support set of the distribution, and construct asymptotical bounds for the expected optimal cost.

Original languageEnglish (US)
Pages (from-to)525-551
Number of pages27
JournalMathematical Programming
Volume109
Issue number2-3
DOIs
StatePublished - Mar 1 2007
Externally publishedYes

Keywords

  • Asymptotical analysis
  • Convergence bounds
  • Expected optimal value
  • Multidimensional assignment problem
  • Random assignment problem

ASJC Scopus subject areas

  • Software
  • Mathematics(all)

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