Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reducing the rank of a matroid   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.

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The categories of this paper are: bayes-an
3
The categories of this paper are: physics
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The categories of this paper are: solv-int
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: q-fin
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The categories of this paper are: ao-sci