Performance ratios of the Karmarkar-Karp differencing method

Wil Michiels (), Jan Korst, Emile Aarts and Jan van Leeuwen
Additional contact information
Wil Michiels: Philips Research Laboratories
Jan Korst: Philips Research Laboratories
Emile Aarts: Philips Research Laboratories
Jan van Leeuwen: Utrecht University

Journal of Combinatorial Optimization, 2007, vol. 13, issue 1, No 2, 19-32

Abstract: Abstract We consider the multiprocessor scheduling problem in which one must schedule n independent tasks nonpreemptively on m identical, parallel machines, such that the completion time of the last task is minimal. For this well-studied problem the Largest Differencing Method of Karmarkar and Karp outperforms other existing polynomial-time approximation algorithms from an average-case perspective. For m ≥ 3 the worst-case performance of the Largest Differencing Method has remained a challenging open problem. In this paper we show that the worst-case performance ratio is bounded between $$ frac{4}{3}-\frac{1}{3(m-1)}$ and $\frac{4}{3}-\frac{1}{3m}$$ . For fixed m we establish further refined bounds in terms of n.

Keywords: LDM; Differencing method; Worst-case performance; Multiprocessor scheduling; Number partitioning (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1007/s10878-006-9010-z

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