Exchange Properties of M-natural-concave Set Functions and Valuated Matroids
Kazuo Murota
TL;DR
This survey reviews exchange properties of M-natural-concave set functions and valuated matroids, consolidating scattered results and providing elementary proofs to clarify their foundational principles.
Contribution
It compiles and simplifies existing results on exchange properties of M-natural-concave functions and valuated matroids, making them more accessible.
Findings
Consolidation of exchange property results
Elementary proofs for key properties
Clarification of foundational principles
Abstract
This is a survey article on the exchange properties characterizing M-natural-concave set functions and valuated matroids (M-concave set functions). The objective of this paper is to collect related results scattered in the literature and to give (reasonably) self-contained elementary proofs for them.
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Taxonomy
TopicsComplexity and Algorithms in Graphs · Rough Sets and Fuzzy Logic · Advanced Graph Theory Research