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

5 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

Access to Document

10.1007/s13160-012-0082-0

Cite this

@article{c2370a442ab9458dbcc838b9ecd15f8b,

title = "Matroid rank functions and discrete concavity",

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.",

keywords = "Combinatorial optimization, Discrete concave function, Matroid, Rank function, Submodular function",

author = "Akiyoshi Shioura",

note = "Funding Information: This work is partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.",

year = "2012",

month = oct,

doi = "10.1007/s13160-012-0082-0",

language = "English",

volume = "29",

pages = "535--546",

journal = "Japan Journal of Industrial and Applied Mathematics",

issn = "0916-7005",

publisher = "Springer Japan",

number = "3",

}

TY - JOUR

T1 - Matroid rank functions and discrete concavity

AU - Shioura, Akiyoshi

N1 - Funding Information: This work is partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan.

PY - 2012/10

Y1 - 2012/10

N2 - 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.

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

KW - Matroid

KW - Rank function

KW - Submodular function

UR - http://www.scopus.com/inward/record.url?scp=84870940150&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870940150&partnerID=8YFLogxK

U2 - 10.1007/s13160-012-0082-0

DO - 10.1007/s13160-012-0082-0

M3 - Article

AN - SCOPUS:84870940150

VL - 29

SP - 535

EP - 546

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 3

ER -

Matroid rank functions and discrete concavity

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this