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Author Peres, Yuval ♦ Sotnikov, Dmitry ♦ Sudakov, Benny ♦ Zwick, Uri
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2013
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Shortest paths ♦ Probabilistic analysis
Abstract We present an all-pairs shortest path algorithm whose running time on a complete directed graph on $\textit{n}$ vertices whose edge weights are chosen independently and uniformly at random from [0,1] is $O(n^{2}),$ in expectation and with high probability. This resolves a long-standing open problem. The algorithm is a variant of the dynamic all-pairs shortest paths algorithm of Demetrescu and Italiano [2006]. The analysis relies on a proof that the number of locally shortest paths in such randomly weighted graphs is $O(n^{2}),$ in expectation and with high probability. We also present a dynamic version of the algorithm that recomputes all shortest paths after a random edge update in $O(log^{2}n)$ expected time.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2013-09-04
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 60
Issue Number 4
Page Count 25
Starting Page 1
Ending Page 25

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Source: ACM Digital Library