Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Complexity of Leader Election: A Chasm at Diameter Two   This paper focuses on studying the message complexity of implicit leader
election in synchronous distributed networks of diameter two. Kutten et al.\
[JACM 2015] showed a fundamental lower bound of $\Omega(m)$ ($m$ is the number
of edges in the network) on the message complexity of (implicit) leader
election that applied also to Monte Carlo randomized algorithms with constant
success probability; this lower bound applies for graphs that have diameter at
least three. On the other hand, for complete graphs (i.e., graphs with diameter
one), Kutten et al.\ [TCS 2015] established a tight bound of
$\tilde{\Theta}(\sqrt{n})$ on the message complexity of randomized leader
election ($n$ is the number of nodes in the network). For graphs of diameter
two, the complexity was not known.
  In this paper, we settle this complexity by showing a tight bound of
$\tilde{\Theta}(n)$ on the message complexity of leader election in
diameter-two networks. Together with the two previous results of Kutten et al.,
our results fully characterize the message complexity of leader election
vis-\`a-vis the graph diameter.

21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
2
The categories of this paper are: math
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
25
The categories of this paper are: patt-sol
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph