The differencing algorithm LDM for partitioning: A proof of a conjecture of Karmarkar and Karp

Benjamin Yakir

doi:10.1287/moor.21.1.85

The differencing algorithm LDM for partitioning: A proof of a conjecture of Karmarkar and Karp

Benjamin Yakir^*

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

30 Scopus citations

Abstract

The algorithm LDM (largest differencing method) divides a list of n random items into two blocks. The parameter of interest is the expected difference between the two block sums. It is shown that if the items are i.i.d. and uniform then the rate of convergence of this parameter to zero is n^{-Θ(log n)}. An algorithm for balanced partitioning is constructed, with the same rate of convergence to zero.

Original language	English
Pages (from-to)	85-99
Number of pages	15
Journal	Mathematics of Operations Research
Volume	21
Issue number	1
DOIs	https://doi.org/10.1287/moor.21.1.85
State	Published - Feb 1996

Keywords

Differencing method
Makespan
Partitioning
Probabilistic analysis of algorithms
Scheduling

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The differencing algorithm LDM for partitioning: A proof of a conjecture of Karmarkar and Karp

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Keywords

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