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 |
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Pages (from-to) | 535-546 |
Number of pages | 12 |
Journal | Japan Journal of Industrial and Applied Mathematics |
Volume | 29 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2012 Oct |
Keywords
- Combinatorial optimization
- Discrete concave function
- Matroid
- Rank function
- Submodular function
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics