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Volume 18, No 3, 2011, P. 11-20

UDC 519.8
E. Kh. Gimadi, V. T. Dementiev
Probabilistic analysis of decentralized version of ne generalization of the assignment problem

Abstract:
A decentralized version of the Semi-Assignment problem is considered, when elements of $m\times n$-matrix are nonnegative, $m=kn$, $k$ is natural number. It is supposed, that $nk$ elements of the matrix are chosen: $k$ elements in each column and one element in each row in order to maximize the total sum of chosen elements. An approximation algorithm with $O(mn)$ time complexity is presented. In the case of inputs, when elements are independent random values with common uniform distribution function, the estimations of a relative error and a fault probability of the algorithm are obtained, and conditions of asymptotic optimality are established.
Bibliogr. 8.

Keywords: decentralized transportation problem, NP-hardness, approximation algorithm, asymptotic optimality, Petrov’s theorem, uniform distribution.

Gimadi Eduard Khirutdinovich 1,2
Dementev Vladimir Tikhonovich 1,2

1. S. L. Sobolev Institute of Mathematics, SB RAS,
4 Acad. Koptyug Ave., 630090 Novosibirsk, Russia
2. Novosibirsk State University,
2 Pirogov St., 630090 Novosibirsk, Russia
e-mail: gimadi@math.nsc.ru, dementev@math.nsc.ru

 © Sobolev Institute of Mathematics, 2015