Learning to solve Minimum Cost Multicuts efficiently using Edge-Weighted Graph Convolutional Neural Networks

TL;DR

This paper introduces a novel end-to-end trainable GNN-based method for solving the NP-hard minimum cost multicut problem efficiently, outperforming traditional LP solvers and heuristics especially on large graphs.

Contribution

It adapts various GNN architectures for real-valued edge weights and reformulates multicut constraints into a polynomial program as a loss function for scalable learning.

Findings

GNN approaches produce good solutions in practice.

Significant reduction in computation time.

Enhanced scalability on large instances.

Abstract

The minimum cost multicut problem is the NP-hard/APX-hard combinatorial optimization problem of partitioning a real-valued edge-weighted graph such as to minimize the total cost of the partition. While graph convolutional neural networks (GNN) have proven to be promising in the context of combinatorial optimization, most of them are only tailored to or tested on positive-valued edge weights, i.e. they do not comply to the nature of the multicut problem. We therefore adapt various GNN architectures including Graph Convolutional Networks, Signed Graph Convolutional Networks and Graph Isomorphic Networks to facilitate the efficient encoding of real-valued edge costs. Moreover, we employ a reformulation of the multicut ILP constraints to a polynomial program as loss function that allows to learn feasible multicut solutions in a scalable way. Thus, we provide the first approach towards end-to-end trainable multicuts. Our findings support that GNN approaches can produce good solutions in practice while providing lower computation times and largely improved scalability compared to LP solvers and optimized heuristics, especially when considering large instances.