




Analysis of the KarmarkarKarp Differencing Algorithm
Stefan Boettcher and
Stephan Mertens
Abstract
The KarmarkarKarp differencing algorithm is the best known polynomial time heuristic for the number partitioning problem, fundamental in both theoretical computer science and statistical physics. We analyze the performance of the differencing algorithm on random instances by mapping it to a nonlinear rate equation. Our analysis reveals strong finite size effects that explain why the precise asymptotics of the differencing solution is hard to establish by simulations. The asymptotic series emerging from the rate equation satisfies all known bounds on the KarmarkarKarp algorithm and projects a scaling $n^{c\ln n}$, where $c=1/(2\ln2)=0.7213\ldots$. Our calculations reveal subtle relations between the algorithm and Fibonaccilike sequences, and we establish an explicit identity to that effect.
BiBTeX Entry
@article{kk:08, author = {Stefan Boettcher and Stephan Mertens}, title = {Analysis of the {K}armarkar{K}arp Differencing Algorithm}, journal = {European Physics Journal B}, vol = {65}, year = {2008}, pages = {131140} }
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© by Stephan Mertens
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updated on Wednesday, September 10th 2008, 16:31:28 CET;