Abstract
AbstractChapter 5 studies the problem of whether all Boolean submodular functions can be decomposed into a sum of binary submodular functions over a possibly larger set of variables. This problem has been considered within several different contexts in computer science, including computer vision, artificial intelligence, and pseudo-Boolean optimisation. Using the connection between the expressive power of submodular functions and certain algebraic properties of functions described in earlier chapters, a negative answer to this question is shown. Consequently, there are submodular functions that cannot be reduced to the minimum cut problem via the expressibility reduction.KeywordsSubmodular Cost FunctionsPseudo-boolean OptimizationMultimorphismFractional PolymorphismsHigher Order Energy FunctionsThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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