Submodularity of a Set Label Disagreement Function

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.