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arXiv · 2110.08886

On Monotonicity of Number-Partitioning Algorithms

Erel Segal-Halevi
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Abstract

An algorithm for number-partitioning is called value-monotone if whenever one of the input numbers increases, the objective function (the largest sum or the smallest sum of a subset in the output) weakly increases. This note proves that the List Scheduling algorithm and the Longest Processing Time algorithm are both value-monotone. This is in contrast to another algorithm -- MultiFit -- which is not value-monotone.

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Erel Segal-Halevi. 2021-10-17. On Monotonicity of Number-Partitioning Algorithms. https://arxiv.org/abs/2110.08886

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