Convergent sequences of combinatorial submodular setfunctions

TL;DR

This paper explores the convergence properties of sequences of combinatorial submodular setfunctions, demonstrating their relevance to graph limit theory through various classes of matroids and submodular functions.

Contribution

It establishes convergence results for sequences of submodular functions, linking combinatorial optimization with graph limit theory, and provides nontrivial proofs for these convergence properties.

Findings

Convergence of submodular function sequences can be established for certain classes.

The results connect submodular functions with graph limit theory.

Some proofs of convergence are notably complex.

Abstract

To illustrate that the notion of convergence of submodular function sequences fits reasonably into the limit theory of graphs, we describe several classes of matroids and other submodular setfunctions for which convergence of appropriate sequences can be proved. Some of the proofs are surprisingly nontrivial.