On Monotonicity of Number-Partitioning Algorithms

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.

arXiv commentI needed this lemma for something else, and could not find it anywhere, so I wrote a short proof. Is it already known?