On Monotonicity of Number-Partitioning Algorithms
Data Structures and Algorithms
2021-10-19 v1
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.
Keywords
Cite
@article{arxiv.2110.08886,
title = {On Monotonicity of Number-Partitioning Algorithms},
author = {Erel Segal-Halevi},
journal= {arXiv preprint arXiv:2110.08886},
year = {2021}
}
Comments
I needed this lemma for something else, and could not find it anywhere, so I wrote a short proof. Is it already known?