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Probabilistic analysis of optimum partitioning

Published online by Cambridge University Press:  14 July 2016

Narendra Karmarkar ,
Richard M. Karp ,
George S. Lueker  and
Andrew M. Odlyzko
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
*
∗ Postal address: AT&T Bell Laboratories, Murray Hill, NJ 07974, USA.
∗∗ Postal address: Dept. of Electrical Engineering and Computer Science, University of California, Berkeley, CA 94720, USA.
∗∗∗ Postal address: Dept. of Information and Computer Science, University of California, Irvine, CA 92717, USA.
∗ Postal address: AT&T Bell Laboratories, Murray Hill, NJ 07974, USA.
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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.

Keywords

PARTITION PROBLEMSECOND-MOMENT METHODCOMBINATORIAL OPTIMIZATION

Information

Type
Research Paper
Information
Journal of Applied Probability , Volume 23 , Issue 3 , September 1986 , pp. 626 - 645
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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