On the expected optimal value of random assignment problems: Experimental results and open questions

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In the paper, we study the expected optimal value of random linear assignment problems, whose data are random variables with the uniform and the exponential distributions. An interior point approach is used to solve large-scale dense assignment problems with size up to 10,000 nodes and 100 million edges. Our computational results indicate the validity of a long-standing conjecture about the limiting value of the expected optimal assignment. Some interesting open problems and extensions are discussed.