On Monotonicity of Number-Partitioning Algorithms
Erel Segal-Halevi
TL;DR
This paper investigates the monotonicity properties of various number-partitioning algorithms, proving that List Scheduling and Longest Processing Time algorithms are value-monotone, while MultiFit is not, highlighting differences in their behavior.
Contribution
It establishes the monotonicity status of key number-partitioning algorithms, providing theoretical insights into their behavior under input changes.
Findings
List Scheduling is value-monotone.
Longest Processing Time algorithm is value-monotone.
MultiFit algorithm is not value-monotone.
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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Taxonomy
Topicssemigroups and automata theory · Computability, Logic, AI Algorithms · graph theory and CDMA systems