Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Simple Deterministic Distributed MST Algorithm, with Near-Optimal Time
  and Message Complexities   Distributed minimum spanning tree (MST) problem is one of the most central
and fundamental problems in distributed graph algorithms. Garay et al.
\cite{GKP98,KP98} devised an algorithm with running time $O(D + \sqrt{n} \cdot
\log^* n)$, where $D$ is the hop-diameter of the input $n$-vertex $m$-edge
graph, and with message complexity $O(m + n^{3/2})$. Peleg and Rubinovich
\cite{PR99} showed that the running time of the algorithm of \cite{KP98} is
essentially tight, and asked if one can achieve near-optimal running time
**together with near-optimal message complexity**.
  In a recent breakthrough, Pandurangan et al. \cite{PRS16} answered this
question in the affirmative, and devised a **randomized** algorithm with time
$\tilde{O}(D+ \sqrt{n})$ and message complexity $\tilde{O}(m)$. They asked if
such a simultaneous time- and message-optimality can be achieved by a
**deterministic** algorithm.
  In this paper, building upon the work of \cite{PRS16}, we answer this
question in the affirmative, and devise a **deterministic** algorithm that
computes MST in time $O((D + \sqrt{n}) \cdot \log n)$, using $O(m \cdot \log n
+ n \log n \cdot \log^* n)$ messages. The polylogarithmic factors in the time
and message complexities of our algorithm are significantly smaller than the
respective factors in the result of \cite{PRS16}. Also, our algorithm and its
analysis are very **simple** and self-contained, as opposed to rather
complicated previous sublinear-time algorithms \cite{GKP98,KP98,E04b,PRS16}.

35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph