Minimizing Submodular Functions on Diamonds via Generalized Fractional Matroid Matchings

Satoru Fujishige, Tamás Király, Kazuhisa Makino, Kenjiro Takazawa, Shin-ichi Tanigawa


In this paper we show the first polynomial-time algorithm for the problem of minimizing submodular functions on the product of diamonds of finite size. This submodular function minimization problem is reduced to the membership problem for an associated polyhedron, which is equivalent to the optimization problem over the polyhedron, based on the ellipsoid method. The latter optimization problem is a generalization of the weighted fractional matroid matching problem. We give a combinatorial polynomial-time algorithm for this optimization problem by extending the result by Gijswijt and Pap [D. Gijswijt and G. Pap, An algorithm for weighted fractional matroid matching, J. Combin. Theory, Ser. B 103 (2013), 509-520].

Previous versions can be found here and here.

Bibtex entry:

AUTHOR = {Fujishige, Satoru and Kir{\'a}ly, Tam{\'a}s and Makino, Kazuhisa and Takazawa, Kenjiro and Tanigawa, Shin-ichi},
TITLE = {Minimizing Submodular Functions on Diamonds via Generalized Fractional Matroid Matchings},
NOTE= {{\tt}},
INSTITUTION = {Egerv{\'a}ry Research Group, Budapest},
YEAR = {2014},
NUMBER = {TR-2014-14}

Last modification: 29.12.2020. Please email your comments to Tamás Király!