Asymptotic Properties of Random Multidimensional Assignment Problems

D. A. Grundel, C. A. S. Oliveira and P. M. Pardalos
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D. A. Grundel: Eglin Air Force Base
C. A. S. Oliveira: University of Florida
P. M. Pardalos: University of

Journal of Optimization Theory and Applications, 2004, vol. 122, issue 3, No 3, 487-500

Abstract: 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.

Keywords: Multidimensional assignment problem; combinatorial optimization; asymptotic results (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (2)

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DOI: 10.1023/B:JOTA.0000042592.16418.1b

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