Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Deterministic Algorithm for the MST Problem in Constant Rounds of
  Congested Clique   In this paper, we show that the Minimum Spanning Tree problem can be solved
\emph{deterministically}, in $\mathcal{O}(1)$ rounds of the
$\mathsf{Congested}$ $\mathsf{Clique}$ model.
  In the $\mathsf{Congested}$ $\mathsf{Clique}$ model, there are $n$ players
that perform computation in synchronous rounds. Each round consist of a phase
of local computation and a phase of communication, in which each pair of
players is allowed to exchange $\mathcal{O}(\log n)$ bit messages.
  The studies of this model began with the MST problem: in the paper by Lotker
et al.[SPAA'03, SICOMP'05] that defines the $\mathsf{Congested}$
$\mathsf{Clique}$ model the authors give a deterministic $\mathcal{O}(\log \log
n)$ round algorithm that improved over a trivial $\mathcal{O}(\log n)$ round
adaptation of Bor\r{u}vka's algorithm.
  There was a sequence of gradual improvements to this result: an
$\mathcal{O}(\log \log \log n)$ round algorithm by Hegeman et al. [PODC'15], an
$\mathcal{O}(\log^* n)$ round algorithm by Ghaffari and Parter, [PODC'16] and
an $\mathcal{O}(1)$ round algorithm by Jurdzi\'nski and Nowicki, [SODA'18], but
all those algorithms were randomized, which left the question about the
existence of any deterministic $o(\log \log n)$ round algorithms for the
Minimum Spanning Tree problem open.
  Our result resolves this question and establishes that $\mathcal{O}(1)$
rounds is enough to solve the MST problem in the $\mathsf{Congested}$
$\mathsf{Clique}$ model, even if we are not allowed to use any randomness.
Furthermore, the amount of communication needed by the algorithm makes it
applicable to some variants of the $\mathsf{MPC}$ model.

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The categories of this paper are: nlin
16
The categories of this paper are: stat
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The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
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The categories of this paper are: q-alg
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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: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn