Submodularity of a Set Label Disagreement Function

TL;DR

This paper investigates the submodularity property of a set label disagreement function based on dominant labels in binary variable sets, with potential applications in hypergraph optimization.

Contribution

It introduces and analyzes the submodularity of a specific set label disagreement function, expanding tools for combinatorial optimization in hypergraph problems.

Findings

Proves submodularity of the disagreement function under certain conditions

Highlights potential use in hypergraph-based optimization problems

Provides theoretical foundation for future algorithm development

Abstract

A set label disagreement function is defined over the number of variables that deviates from the dominant label. The dominant label is the value assumed by the largest number of variables within a set of binary variables. The submodularity of a certain family of set label disagreement function is discussed in this manuscript. Such disagreement function could be utilized as a cost function in combinatorial optimization approaches for problems defined over hypergraphs.