Matroid parity problem
http://dbpedia.org/resource/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.
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Matroid parity problem
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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.
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