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 | |
| Publication status | Published - 2012 Oct 1 |
Keywords
- Combinatorial optimization
- Discrete concave function
- Matroid
- Rank function
- Submodular function
ASJC Scopus subject areas
- Engineering(all)
- Applied Mathematics
Fingerprint Dive into the research topics of 'Matroid rank functions and discrete concavity'. Together they form a unique fingerprint.
Cite this
Shioura, A. (2012). Matroid rank functions and discrete concavity. Japan Journal of Industrial and Applied Mathematics, 29(3), 535-546. https://doi.org/10.1007/s13160-012-0082-0