Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
On Approximation Methods for the Assignment Problem
Journal of the ACM (JACM)
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J.M. Kurtzberg proposed a method of obtaining approximate solutions to the assignment problem by decomposing a large problem into many smaller subproblems. Thus a km x km assignment problem is decomposed into k^2 problems of size m x m and one problem of size k x k. In this paper we analyze the performance of this heuristic, obtaining the following main results: 1.(1) For the maximization problem, the ratio of the optimal solution to the heuristic solution can be as large as, but cannot exceed min(k, m); 2.(2) For the minimization problem, if k = o(n/log n) where n = mk, and the matrix elements are independently drawn from a uniform distribution on (0, 1), in the limit the expected value of the heuristic solution is at least k/3 times that of the optimal solution.