On Approximation Methods for the Assignment Problem
Journal of the ACM (JACM)
Constructive Bounds and Exact Expectations for the Random Assignment Problem
RANDOM '98 Proceedings of the Second International Workshop on Randomization and Approximation Techniques in Computer Science
An asymptotical study of combinatorial optimization problems by means of statistical mechanics
Journal of Computational and Applied Mathematics - Special issue: Jef Teugels
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A new suboptimal intermediate-speed algorithm which use n2 In n steps is developed for the assignment problem. Upper and lower bounds are derived, using this algorithm and other methods, for the average values of three classes of n × n assignment problems: 1. When the elements of the matrix are random numbers uniformly distributed over the range 0 to 1, the average optimal value is smaller than 2.37 and larger than 1 for problems with large n. Experimentally the value is about 1.6. 2. When the elements of the matrix are random numbers such that the probability of being less than x is xk+1 (k ≠ 0), asymptotic expressions for the upper and lower bounds of the average optimal value are Cknk/(k+1) and Ck[(k+1)/k]nk/(k+1) respectively. 3. When each column of the matrix is a random permutation of the integers 1 to n, asymptotic upper and lower bounds are 2.37n and 1.54n, respectively. Experimentally the value is about 1.8n.