Combinatorial optimization | Matroid theory

Matroid parity problem

In combinatorial optimization, the matroid parity problem is a problem of finding the largest independent set of paired elements in a matroid. The problem was formulated by as a common generalization of graph matching and matroid intersection. It is also known as polymatroid matching, or the matchoid problem. Matroid parity can be solved in polynomial time for linear matroids. However, it is NP-hard for certain compactly-represented matroids, and requires more than a polynomial number of steps in the matroid oracle model. Applications of matroid parity algorithms include finding large planar subgraphs and finding graph embeddings of maximum genus. These algorithms can also be used to find connected dominating sets and feedback vertex sets in graphs of maximum degree three. (Wikipedia).

Matroid parity problem
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Related pages

Spanning tree | Combinatorial optimization | Xuong tree | Matroid rank | Randomized algorithm | Vector space | Linear algebra | Finite set | Planar graph | Planarization | Feedback vertex set | Cactus graph | Graphic matroid | Multigraph | Disjoint sets | Linear independence | Polynomial-time approximation scheme | Determinant | Partition matroid | Genus (mathematics) | Empty set | Sherman–Morrison formula | Matroid | Greedy algorithm | Clique problem | Clique (graph theory) | Induced subgraph | Connected dominating set | Cycle (graph theory) | Cubic graph | Euclidean plane | Schwartz–Zippel lemma | Hypergraph | Graph matching | Approximation algorithm | Paving matroid | Local search (optimization) | Matroid intersection | Graph embedding | Matrix (mathematics) | Matroid oracle | Polymatroid