Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Massively Parallel Algorithm for Minimum Weight Vertex Cover   We present a massively parallel algorithm, with near-linear memory per
machine, that computes a $(2+\varepsilon)$-approximation of minimum-weight
vertex cover in $O(\log\log d)$ rounds, where $d$ is the average degree of the
input graph.
  Our result fills the key remaining gap in the state-of-the-art MPC algorithms
for vertex cover and matching problems; two classic optimization problems,
which are duals of each other. Concretely, a recent line of work---by Czumaj et
al. [STOC'18], Ghaffari et al. [PODC'18], Assadi et al. [SODA'19], and Gamlath
et al. [PODC'19]---provides $O(\log\log n)$ time algorithms for
$(1+\varepsilon)$-approximate maximum weight matching as well as for
$(2+\varepsilon)$-approximate minimum cardinality vertex cover. However, the
latter algorithm does not work for the general weighted case of vertex cover,
for which the best known algorithm remained at $O(\log n)$ time complexity.

2
The categories of this paper are: math
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph