Optimal matroid bases with intersection constraints: valuated matroids, M-convex functions, and their applications

For two matroids M 1 and M 2 with the same ground set V and two cost functions w 1 and w 2 on 2 V , we consider the problem of finding bases X 1 of M 1 and X 2 of M 2 minimizing w 1 ( X 1 ) + w 2 ( X 2 ) subject to a certain cardinality constraint on their intersection X 1 ∩ X 2 . For this problem,...

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Bibliographic Details
Published in:	Mathematical programming Vol. 194; no. 1-2; pp. 229 - 256
Main Authors:	Iwamasa, Yuni, Takazawa, Kenjiro
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2022 Springer Springer Nature B.V
Subjects:	Algorithms Calculus of Variations and Optimal Control; Optimization Combinatorial analysis Combinatorics Convex analysis Cost function Full Length Paper Intersections Mathematical and Computational Physics Mathematical Methods in Physics Mathematics Mathematics and Statistics Mathematics of Computing Numerical Analysis Optimization Theoretical 90C27 (Mathematical programming: Combinatorial optimization Combinatorial optimization problem with interaction costs Congestion game Valuated independent assignment 68Q25 (Theory of computing: Analysis of algorithms and problem complexity) M-convex submodular flow Recoverable robust matroid basis problem Valuated matroid intersection
ISSN:	0025-5610, 1436-4646
Online Access:	Get full text
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