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The Expressive Power of Binary Submodular Functions by Stanislav Živný; David A. Cohen; Peter G. Jeavons is a Computer Science article available to read on EtoBox.

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## a b s t r a c t We investigate whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a possibly larger set of variables. This question has been considered in several different contexts in computer science, including computer vision, artificial intelligence, and pseudo-Boolean optimisation. Using a connection between the expressive power of valued constraints and certain algebraic properties of functions, we answer this question negatively. Our results have several corollaries. First, we characterise precisely which submodular polynomials of arity 4 can be expressed by binary submodular polynomials. Next, we identify a novel class of submodular functions of arbitrary arities which can be expressed by binary submodular functions, and therefore minimised efficiently using a so-called expressibility reduction to the Min-Cut problem. More importantly, our results imply limitations on this kind of reduction and establish, for the first time, that it cannot be used in general to minimise arbitrary submodular functions. Finally, we refute a conjecture of Promislow and Young on the structure of the extreme rays of the cone of Boolean su

Who reads The Expressive Power of Binary Submodular Functions?

Author

Stanislav Živný; David A. Cohen; Peter G. Jeavons

Publisher

Elsevier Science; Elsevier ; Elsevier BV (ISSN 0166-218X)

Published

2009

Language

EN

Field

Computer Science (Physical Sciences)