Heuristic algorithms for balanced multi-way number partitioning

  • Authors:

  • Jilian Zhang;Kyriakos Mouratidis;HweeHwa Pang

  • Affiliations:

  • School of Information Systems, Singapore Management University;School of Information Systems, Singapore Management University;School of Information Systems, Singapore Management University

  • Venue:
  • IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
  • Year:
  • 2011

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Abstract

Balanced multi-way number partitioning (BMNP) seeks to split a collection of numbers into subsets with (roughly) the same cardinality and subset sum. The problem is NP-hard, and there are several exact and approximate algorithms for it. However, existing exact algorithms solve only the simpler, balanced two-way number partitioning variant, whereas the most effective approximate algorithm, BLDM, may produce widely varying subset sums. In this paper, we introduce the LRM algorithm that lowers the expected spread in subset sums to one third that of BLDM for uniformly distributed numbers and odd subset cardinalities. We also propose Meld, a novel strategy for skewed number distributions. A combination of LRM and Meld leads to a heuristic technique that consistently achieves a narrower spread of subset sums than BLDM.