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

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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.

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Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, University of Iowa, Iowa City, IA, 52242, USA

    Pavlo A. Krokhmal

  2. Air Force Research Lab/Munitions Directorate, Eglin AFB, FL, 32542, USA

    Don A. Grundel

  3. Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL, 32611, USA

    Panos M. Pardalos

Authors
  1. Pavlo A. Krokhmal
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  2. Don A. Grundel
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  3. Panos M. Pardalos
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Correspondence to Pavlo A. Krokhmal.

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Partially supported by NSF grant DMI-0457473.

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Krokhmal, P.A., Grundel, D.A. & Pardalos, P.M. Asymptotic behavior of the expected optimal value of the multidimensional assignment problem. Math. Program. 109, 525–551 (2007). https://doi.org/10.1007/s10107-006-0036-x

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  • DOI: https://doi.org/10.1007/s10107-006-0036-x

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