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- W1889776955 abstract "We consider the rank reduction problem for matroids: Given a matroid M and an integer k, find a minimum size subset of elements of M whose removal reduces the rank of M by at least k. When M is a graphical matroid this problem is the minimum k-cut problem, which admits a 2-approximation algorithm. In this paper we show that the rank reduction problem for transversal matroids is essentially at least as hard to approximate as the densest k-subgraph problem. We also prove that, while the problem is easily solvable in polynomial time for partition matroids, it is NP-hard when considering the intersection of two partition matroids. Our proof shows, in particular, that the maximum vertex cover problem is NP-hard on bipartite graphs, which answers an open problem of B. Simeone." @default.
- W1889776955 created "2016-06-24" @default.
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- W1889776955 date "2015-09-16" @default.
- W1889776955 modified "2023-10-16" @default.
- W1889776955 title "Reducing the rank of a matroid" @default.
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- W1889776955 doi "https://doi.org/10.46298/dmtcs.2135" @default.
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