Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Improved Random Shift Algorithm for Spanners and Low Diameter
  Decompositions   Spanners have been shown to be a powerful tool in graph algorithms. Many
spanner constructions use a certain type of clustering at their core, where
each cluster has small diameter and there are relatively few spanner edges
between clusters. In this paper, we provide a clustering algorithm that, given
$k\geq 2$, can be used to compute a spanner of stretch $2k-1$ and expected size
$O(n^{1+1/k})$ in $k$ rounds in the CONGEST model. This improves upon the state
of the art (by Elkin, and Neiman [TALG'19]) by making the bounds on both
running time and stretch independent of the random choices of the algorithm,
whereas they only hold with high probability in previous results. Spanners are
used in certain synchronizers, thus our improvement directly carries over to
such synchronizers. Furthermore, for keeping the \emph{total} number of
inter-cluster edges small in low diameter decompositions, our clustering
algorithm provides the following guarantees. Given $\beta\in (0,1]$, we compute
a low diameter decomposition with diameter bound $O\left(\frac{\log
n}{\beta}\right)$ such that each edge $e\in E$ is an inter-cluster edge with
probability at most $\beta\cdot w(e)$ in $O\left(\frac{\log n}{\beta}\right)$
rounds in the CONGEST model. Again, this improves upon the state of the art (by
Miller, Peng, and Xu [SPAA'13]) by making the bounds on both running time and
diameter independent of the random choices of the algorithm, whereas they only
hold with high probability in previous results.

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The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
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The categories of this paper are: econ
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
2
The categories of this paper are: math
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
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The categories of this paper are: stat
4
The categories of this paper are: cond-mat