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| Content Provider | Society for Industrial and Applied Mathematics (SIAM) |
|---|---|
| Author | Takamatsu, Mizuyo Kakimura, Naonori |
| Copyright Year | 2014 |
| Abstract | Given an undirected graph $G=(V, E)$ and a delta-matroid $(V,{\cal F})$, the delta-matroid matching problem is to find a maximum cardinality matching $M$ such that the set of the end vertices of $M$ belongs to ${\cal F}$. This problem is a natural generalization of the matroid matching problem to delta-matroids, and thus it cannot be solved in polynomial time in general. This paper introduces a class of the delta-matroid matching problem, where the given delta-matroid is a projection of a linear delta-matroid. We first show that it can be solved in polynomial time if the given linear delta-matroid is generic. This result enlarges a polynomially solvable class of matching problems with precedence constraints on vertices such as the 2-master/slave matching. In addition, we design a polynomial-time algorithm when the graph is bipartite and the delta-matroid is defined on one vertex side. This result is extended to the case where a linear matroid constraint is additionally imposed on the other vertex side. |
| Starting Page | 942 |
| Ending Page | 961 |
| Page Count | 20 |
| File Format | |
| ISSN | 08954801 |
| DOI | 10.1137/110860070 |
| e-ISSN | 10957146 |
| Journal | SIAM Journal on Discrete Mathematics (SJDMEC) |
| Issue Number | 2 |
| Volume Number | 28 |
| Language | English |
| Publisher | Society for Industrial and Applied Mathematics |
| Publisher Date | 2014-06-12 |
| Access Restriction | Subscribed |
| Subject Keyword | Factorization, matching, partitioning, covering and packing mixed matrix theory Matroids, geometric lattices delta-matroid polynomial-time algorithm Combinatorial optimization constrained matching |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
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