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arXiv · 1410.8395

Core-based criterion for extreme supermodular functions

M. Studený·T. Kroupa
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Abstract

We give a necessary and sufficient condition for extremality of a supermodular function based on its min-representation by means of (vertices of) the corresponding core polytope. The condition leads to solving a certain simple linear equation system determined by the combinatorial core structure. Our result allows us to characterize indecomposability in the class of generalized permutohedra. We provide an in-depth comparison between our result and the description of extremality in the supermodular/submodular cone achieved by other researchers.

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M. Studený, T. Kroupa. 2016-06-27. Core-based criterion for extreme supermodular functions. https://arxiv.org/abs/1410.8395

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