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Probabilistic analysis of optimum partitioning

Published online by Cambridge University Press:  14 July 2016

Narendra Karmarkar
Affiliation:
AT&T Bell Laboratories
Richard M. Karp
Affiliation:
University of California, Berkeley
George S. Lueker
Affiliation:
University of California, Irvine
Andrew M. Odlyzko
Affiliation:
AT&T Bell Laboratories

Abstract

Given a set of n items with real-valued sizes, the optimum partition problem asks how it can be partitioned into two subsets so that the absolute value of the difference of the sums of the sizes over the two subsets is minimized. We present bounds on the probability distribution of this minimum under the assumption that the sizes are independent random variables drawn from a common distribution. For a large class of distributions, we determine the asymptotic behavior of the median of this minimum, and show that it is exponentially small.

Type
Research Paper
Copyright
Copyright © Applied Probability Trust 1986 

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Footnotes

Supported by NSF Grant MCS 81-05217 at the University of California at Berkeley.

Supported by NSF Grants MCS 79-04997 and DCR 85-09667 at the University of California at Irvine.

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