On linear programs with random costs
Mathematical Programming: Series A and B
A lower bound on the expected cost of an optimal assignment
Mathematics of Operations Research
Average case analysis of a heuristic for the assignment problem
Mathematics of Operations Research
The random bipartite nearest neighbor graphs
Random Structures & Algorithms - Special issue on statistical physics methods in discrete probability, combinatorics, and theoretical computer science
Algorithm and average-value bounds for assignment problems
IBM Journal of Research and Development
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The random assignment problem is to choose a minimum-cost perfect matching in a complete n × n bipartite graph, whose edge weights are chosen randomly from some distribution such as the exponential distribution with mean 1. In this case it is known that the expectation does not grow unboundedly with n, but approaches a limiting value c* between 1.51 and 2. The limit is conjectured to be c* = π2/6, while a recent conjecture has it that for finite n, the expected cost is EA* = Σi=1n1/i2. By defining and analyzing a constructive algorithm, we show that the limiting expectation is c* n conjecture to partial assignments on complete m × n bipartite graphs, and prove it in some limited cases. A full version of our work is available as [CS98].