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 relaxations, 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.
Swoboda and Andres REF propose a dual decomposition and linear program relaxation algorithm.
A Message Passing Algorithm for the Minimum Cost Multicut Problem
2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)
Mathematics Computer Science