Lov\'asz extension and graph cut

TL;DR

This paper introduces a set-pair Lovász extension to transform graph k-cut problems into equivalent continuous optimization problems, facilitating new approaches to solving these graph partitioning challenges.

Contribution

The paper develops a novel set-pair Lovász extension that provides a continuous optimization framework for graph k-cut problems, bridging discrete and continuous methods.

Findings

Established a set-pair Lovász extension for graph k-cut problems

Provided an equivalent continuous optimization formulation for graph cuts

Facilitated new solution approaches for graph partitioning

Abstract

A set-pair Lov\'asz extension is established to construct equivalent continuous optimization problems for graph $k$-cut problems.