Classes of submodular constraints expressible by graph cuts.

Journal article

Submodular constraints play an important role both in theory and practice of valued constraint satisfaction problems (VCSPs). It has previously been shown, using results from the theory of combinatorial optimisation, that instances of VCSPs with submodular constraints can be minimised in polynomial time. However, the general algorithm is of order O(n6) and hence rather impractical. In this paper, by using results from the theory of pseudo-Boolean optimisation, we identify several broad classes of submodular constraints over a Boolean domain which are expressible using binary submodular constraints, and hence can be minimised in cubic time. Furthermore, we describe how our results translate to certain optimisation problems arising in computer vision. © Springer Science + Business Media, LLC 2009.

Authors: Zivny, S; Jeavons, P

• Journal: Constraints
• Volume: 15
• Issue: 3
• Pages: 430-452
• Publication date: 2010-01-01
• DOI: 10.1007/s10601-009-9078-z
• EISSN: 1572-9354
• ISSN: 1383-7133
• Language: English
• Keywords: Min-cut; Valued constraint satisfaction problems; Minimisation of submodular functions; Pseudo-Boolean optimization; Submodular constraints