A Message Passing Algorithm for the Minimum Cost Multicut Problem

TL;DR

This paper introduces a message passing algorithm for the NP-hard minimum cost multicut problem, offering a more efficient alternative to existing linear programming-based methods, with applications in vision, biomedical imaging, and data mining.

Contribution

It presents a novel dual decomposition and linear program relaxation approach that enables efficient message passing for the multicut problem, improving over state-of-the-art algorithms.

Findings

Algorithm outperforms existing LP-based methods in large instances

Efficient cycle and odd-wheel inequality separation improves convergence

Applicable to real-world problems in vision, biomedical imaging, and data mining

Abstract

We propose a dual decomposition and linear program relaxation of the NP -hard minimum cost multicut problem. Unlike other polyhedral relaxations of the multicut polytope, it is amenable to efficient optimization by message passing. Like other polyhedral elaxations, it can be tightened efficiently by cutting planes. We define an algorithm that alternates between message passing and efficient separation of cycle- and odd-wheel inequalities. This algorithm is more efficient than state-of-the-art algorithms based on linear programming, including algorithms written in the framework of leading commercial software, as we show in experiments with large instances of the problem from applications in computer vision, biomedical image analysis and data mining.