Core-based criterion for extreme supermodular functions
Combinatorics
2016-06-28 v2
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.
Cite
@article{arxiv.1410.8395,
title = {Core-based criterion for extreme supermodular functions},
author = {M. Studený and T. Kroupa},
journal= {arXiv preprint arXiv:1410.8395},
year = {2016}
}