Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Time- and Message-Optimal Distributed Algorithm for Minimum Spanning
  Trees   This paper presents a randomized Las Vegas distributed algorithm that
constructs a minimum spanning tree (MST) in weighted networks with optimal (up
to polylogarithmic factors) time and message complexity. This algorithm runs in
$\tilde{O}(D + \sqrt{n})$ time and exchanges $\tilde{O}(m)$ messages (both with
high probability), where $n$ is the number of nodes of the network, $D$ is the
diameter, and $m$ is the number of edges. This is the first distributed MST
algorithm that matches \emph{simultaneously} the time lower bound of
$\tilde{\Omega}(D + \sqrt{n})$ [Elkin, SIAM J. Comput. 2006] and the message
lower bound of $\Omega(m)$ [Kutten et al., J.ACM 2015] (which both apply to
randomized algorithms).
  The prior time and message lower bounds are derived using two completely
different graph constructions; the existing lower bound construction that shows
one lower bound {\em does not} work for the other. To complement our algorithm,
we present a new lower bound graph construction for which any distributed MST
algorithm requires \emph{both} $\tilde{\Omega}(D + \sqrt{n})$ rounds and
$\Omega(m)$ messages.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
2
The categories of this paper are: math
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn