Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How to Elect a Leader Faster than a Tournament   The problem of electing a leader from among $n$ contenders is one of the
fundamental questions in distributed computing. In its simplest formulation,
the task is as follows: given $n$ processors, all participants must eventually
return a win or lose indication, such that a single contender may win. Despite
a considerable amount of work on leader election, the following question is
still open: can we elect a leader in an asynchronous fault-prone system faster
than just running a $\Theta(\log n)$-time tournament, against a strong adaptive
adversary?
  In this paper, we answer this question in the affirmative, improving on a
decades-old upper bound. We introduce two new algorithmic ideas to reduce the
time complexity of electing a leader to $O(\log^* n)$, using $O(n^2)$
point-to-point messages. A non-trivial application of our algorithm is a new
upper bound for the tight renaming problem, assigning $n$ items to the $n$
participants in expected $O(\log^2 n)$ time and $O(n^2)$ messages. We
complement our results with lower bound of $\Omega(n^2)$ messages for solving
these two problems, closing the question of their message complexity.

35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
28
The categories of this paper are: alg-geom