0459059 20240103212205.820160429235959.9 84959303518 000376542600014 10.1016/j.dam.2016.01.019 29 s. P cav_un_epca*02564970166-218X2061 (2016)122-151Elsevier supermodular function submodular function core conditional independence generalized permutohedron indecomposable polytope cav_un_auth*0101202 Studený Milan Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. cav_un_auth*0101141 Kroupa Tomáš Matematická teorie rozhodování Department of Decision Making Theory MTR MTR UTIA-B Department of Decision Making Theory Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2016/MTR/studeny-0459059.pdf cav_un_auth*0292670 GA13-20012S GA ČR cav_un_auth*0330270 622645 EC 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. This 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. BA 2017 2 4 A hod 4ah 20231122141648.7 RVO:67985556 http://hdl.handle.net/11104/0259703 1 Department of Decision Making Theory UTIA-B 10102 MATHEMATICS, APPLIED S 2 Article Mathematics Applied MATHEMATICS.APPLIED 0.962 0.17 10 0.01268 0.578 5253 0.863 Q2 0.785 365 Q2 40.46 53.9 Q3 Q2 53.922 2016 Soubory v repozitáři: studeny-0459059.pdf 84959303518 SCOPUS 000376542600014 WOS cav_un_epca*0256497 Discrete Applied Mathematics 0166-218X 1872-6771 Roč. 206 č. 1 2016 122 151 Elsevier