RC 21354 (97336) Revised 10/27/99
Computer Science / Mathematics
IBM Research Report On the Expected Incremental Cost of a Minimum Assignment Don Coppersmith, Gregory B. Sorkin IBM T.J. Watson Research Center P.O. Box 218 Yorktown Heights, New York 10598
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ON THE EXPECTED INCREMENTAL COST OF A MINIMUM ASSIGNMENT DON COPPERSMITH AND GREGORY B. SORKIN
Abstract
The random assignment problem is to choose a minimum-cost matching in a complete bipartite graph whose edge weights are chosen randomly from some distribution, such as the exponential distribution with parameter 1. When choosing a perfect matching in the P complete n n bipartite graph, it has been conjectured that the expected cost is ni=1 1=i2 , tending to 2 =6 in the limit. A subsequent, stronger conjecture is that the expectation of a minimum-cost P matching of cardinality k in a complete m n bipartite graph is F(k; m; n) i;j 0; i+j
