Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hitting Diamonds and Growing Cacti   We consider the following NP-hard problem: in a weighted graph, find a
minimum cost set of vertices whose removal leaves a graph in which no two
cycles share an edge. We obtain a constant-factor approximation algorithm,
based on the primal-dual method. Moreover, we show that the integrality gap of
the natural LP relaxation of the problem is \Theta(\log n), where n denotes the
number of vertices in the graph.

5
The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: supr-con
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn