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arXiv · 1901.07167

On random multi-dimensional assignment problems

Alan Frieze·Wesley Pegden·Tomasz Tkocz
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Abstract

We study random multidimensional assignment problems where the costs decompose into the sum of independent random variables. In particular, in three dimensions, we assume that the costs $W_{i,j,k}$ satisfy $W_{i,j,k}=a_{i,j}+b_{i,k}+c_{j,k}$ where the $a_{i,j},b_{i,k},c_{j,k}$ are independent exponential rate 1 random variables. Our objective is to minimize the total cost and we show that w.h.p. a simple greedy algorithm is a $(3+o(1))$-approximation. This is in contrast to the case where the $W_{i,j,k}$ are independent exponential rate 1 random variables. Here all that is known is an $n^{o(1)}$-approximation, due to Frieze and Sorkin.

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Alan Frieze, Wesley Pegden, Tomasz Tkocz. 2019-01-22. On random multi-dimensional assignment problems. https://arxiv.org/abs/1901.07167

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