Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A 2/3-Approximation Algorithm for Vertex-weighted Matching in Bipartite
  Graphs   We consider the maximum vertex-weighted matching problem (MVM), in which
non-negative weights are assigned to the vertices of a graph, the weight of a
matching is the sum of the weights of the matched vertices, and we are required
to compute a matching of maximum weight. We describe an exact algorithm for MVM
with $O(|V|\, |E|)$ time complexity, and then we design a $2/3$-approximation
algorithm for MVM on bipartite graphs by restricting the length of augmenting
paths to at most three. The latter algorithm has time complexity $O(|E| + |V|
\log |V|)$.
  The approximation algorithm solves two MVM problems on bipartite graphs, each
with weights only on one vertex part, and then finds a matching from these two
matchings using the Mendelsohn-Dulmage Theorem. The approximation ratio of the
algorithm is obtained by considering failed vertices, i.e., vertices that the
approximation algorithm fails to match but the exact algorithm does. We show
that at every step of the algorithm there are two distinct heavier vertices
that we can charge each failed vertex to.
  We have implemented the $2/3$-approximation algorithm for MVM and compare it
with four other algorithms: an exact MEM algorithm, the exact MVM algorithm, a
$1/2$-approximation algorithm for MVM, and a scaling-based
$(1-\epsilon)$-approximation algorithm for MEM. We also show that MVM problems
should not be first transformed to MEM problems and solved using exact
algorithms for the latter, since this transformation can increase runtimes by
several orders of magnitude.

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The categories of this paper are: cond-mat
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The categories of this paper are: eess
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-ex
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: atom-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph