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Asymptotic Properties of Random Multidimensional Assignment Problems

Author

Listed:
  • D. A. Grundel

    (Eglin Air Force Base
    University of Florida)

  • C. A. S. Oliveira

    (University of Florida)

  • P. M. Pardalos

    (University of)

Abstract

The multidimensional assignment problem (MAP) is a NP-hard combinatorial optimization problem, occurring in many applications, such as data association. In this paper, we prove two conjectures made in Ref. 1 and based on data from computational experiments on MAPs. We show that the mean optimal objective function cost of random instances of the MAP goes to zero as the problem size increases, when assignment costs are independent exponentially or uniformly distributed random variables. We prove also that the mean optimal solution goes to negative infinity when assignment costs are independent normally distributed random variables.

Suggested Citation

  • D. A. Grundel & C. A. S. Oliveira & P. M. Pardalos, 2004. "Asymptotic Properties of Random Multidimensional Assignment Problems," Journal of Optimization Theory and Applications, Springer, vol. 122(3), pages 487-500, September.
    • Handle: RePEc:spr:joptap:v:122:y:2004:i:3:d:10.1023_b:jota.0000042592.16418.1b
    DOI: 10.1023/B:JOTA.0000042592.16418.1b
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    References listed on IDEAS

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    1. William P. Pierskalla, 1968. "Letter to the Editor—The Multidimensional Assignment Problem," Operations Research, INFORMS, vol. 16(2), pages 422-431, April.
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    Cited by:

    1. Krokhmal, Pavlo A. & Pardalos, Panos M., 2009. "Random assignment problems," European Journal of Operational Research, Elsevier, vol. 194(1), pages 1-17, April.
    2. Walteros, Jose L. & Vogiatzis, Chrysafis & Pasiliao, Eduardo L. & Pardalos, Panos M., 2014. "Integer programming models for the multidimensional assignment problem with star costs," European Journal of Operational Research, Elsevier, vol. 235(3), pages 553-568.

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