PROBABILISTIC ANALYSIS OF OPTIMUM PARTITIONING.

Narendra Karmarkar; Richard M. Karp; George S. Lueker; Andrew M. Odlyzko

doi:10.1017/S0021900200111799

PROBABILISTIC ANALYSIS OF OPTIMUM PARTITIONING.

Narendra Karmarkar, Richard M. Karp, George S. Lueker, Andrew M. Odlyzko

Mathematics

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44 Scopus citations

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.

Original language	English (US)
Pages (from-to)	626-645
Number of pages	20
Journal	Journal of Applied Probability
Volume	23
Issue number	3
DOIs	https://doi.org/10.1017/S0021900200111799
State	Published - 1986

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PROBABILISTIC ANALYSIS OF OPTIMUM PARTITIONING.

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