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On random multi-dimensional assignment problems

by   Alan Frieze, et al.

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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