Matroid rank functions and discrete concavity

Akiyoshi Shioura

doi:10.1007/s13160-012-0082-0

Matroid rank functions and discrete concavity

Akiyoshi Shioura

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We discuss the relationship between matroid rank functions and a concept of discrete concavity called M-concavity. It is known that a matroid rank function and its weighted version called a weighted rank function are M-concave functions, while the (weighted) sum of matroid rank functions is not M-concave in general.We present a sufficient condition for a weighted sum of matroid rank functions to be an M-concave function, and show that every weighted rank function can be represented as a weighted sum of matroid rank functions satisfying this condition.

Original language	English
Pages (from-to)	535-546
Number of pages	12
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s13160-012-0082-0
Publication status	Published - 2012 Oct

Keywords

Combinatorial optimization
Discrete concave function
Matroid
Rank function
Submodular function

ASJC Scopus subject areas

Engineering(all)
Applied Mathematics

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10.1007/s13160-012-0082-0

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AB - We discuss the relationship between matroid rank functions and a concept of discrete concavity called M-concavity. It is known that a matroid rank function and its weighted version called a weighted rank function are M-concave functions, while the (weighted) sum of matroid rank functions is not M-concave in general.We present a sufficient condition for a weighted sum of matroid rank functions to be an M-concave function, and show that every weighted rank function can be represented as a weighted sum of matroid rank functions satisfying this condition.

KW - Combinatorial optimization

KW - Discrete concave function

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KW - Rank function

KW - Submodular function

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Matroid rank functions and discrete concavity

Abstract

Keywords

ASJC Scopus subject areas

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