Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Parallel Shortest-Paths Using Radius Stepping   The single-source shortest path problem (SSSP) with nonnegative edge weights
is a notoriously difficult problem to solve efficiently in parallel---it is one
of the graph problems said to suffer from the transitive-closure bottleneck. In
practice, the $\Delta$-stepping algorithm of Meyer and Sanders (J. Algorithms,
2003) often works efficiently but has no known theoretical bounds on general
graphs. The algorithm takes a sequence of steps, each increasing the radius by
a user-specified value $\Delta$. Each step settles the vertices in its annulus
but can take $\Theta(n)$ substeps, each requiring $\Theta(m)$ work ($n$
vertices and $m$ edges).
  In this paper, we describe Radius-Stepping, an algorithm with the best-known
tradeoff between work and depth bounds for SSSP with nearly-linear
($\otilde(m)$) work. The algorithm is a $\Delta$-stepping-like algorithm but
uses a variable instead of fixed-size increase in radii, allowing us to prove a
bound on the number of steps. In particular, by using what we define as a
vertex $k$-radius, each step takes at most $k+2$ substeps. Furthermore, we
define a $(k, \rho)$-graph property and show that if an undirected graph has
this property, then the number of steps can be bounded by $O(\frac{n}{\rho}
\log \rho L)$, for a total of $O(\frac{kn}{\rho} \log \rho L)$ substeps, each
parallel. We describe how to preprocess a graph to have this property.
Altogether, Radius-Stepping takes $O((m+n\log n)\log \frac{n}{\rho})$ work and
$O(\frac{n}{\rho}\log n \log (\rho{}L))$ depth per source after preprocessing.
The preprocessing step can be done in $O(m\log n + n\rho^2)$ work and
$O(\rho^2)$ depth or in $O(m\log n + n\rho^2\log n)$ work and $O(\rho\log
\rho)$ depth, and adds no more than $O(n\rho)$ edges.

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The categories of this paper are: dg-ga
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: eess