Cut Facets and Cube Facets of Lifted Multicut Polytopes

arXiv:2402.16814v2 Announce Type: replace-cross
Abstract: The lifted multicut problem has diverse applications in the field of computer vision. Exact algorithms based on linear programming require an understanding of lifted multicut polytopes. Despite recent progress, two fundamental questions about these polytopes have remained open: Which lower cube inequalities define facets, and which cut inequalities define facets? In this article, we answer the first question by establishing conditions that are necessary, sufficient and efficiently decidable. Toward the second question, we show that …

abstract algorithms applications arxiv computer computer vision cs.dm cs.lg diverse diverse applications linear programming progress questions type understanding vision