Heuristic Algorithms for Balanced Multi-way Number Partitioning

• Main Authors: ZHANG, Jilian, MOURATIDIS, Kyriakos, PANG, Hwee Hwa
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2011
• Subjects: Approximate algorithms; Cardinalities; Exact algorithms; Heuristic techniques; Novel strategies; Number distribution; Number partitioning; Subset sum; Databases and Information Systems; Theory and Algorithms
• Online Access: https://ink.library.smu.edu.sg/sis_research/1359; https://ink.library.smu.edu.sg/context/sis_research/article/2358/viewcontent/IJCAI11.pdf
• Institution: Singapore Management University

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.