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Author Thorup, Mikkel ♦ Zwick, Uri
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2005
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Approximate distance oracles ♦ Distance labelings ♦ Distance queries ♦ Distances ♦ Shortest paths ♦ Spanners
Abstract Let $\textit{G}$ = $\textit{(V,E)}$ be an undirected $\textit{weighted}$ graph with $|\textit{V}|$ = $\textit{n}$ and $|\textit{E}|$ = $\textit{m}.$ Let $\textit{k}$ ≥ 1 be an integer. We show that $\textit{G}$ = $\textit{(V,E)}$ can be preprocessed in $O(kmn^{1/k})$ expected time, constructing a data structure of size $O(kn^{1+1/k}),$ such that any subsequent distance query can be answered, approximately, in $\textit{O(k)}$ time. The approximate distance returned is of stretch at most $\textit{2k}™1,$ that is, the quotient obtained by dividing the estimated distance by the actual distance lies between 1 and $\textit{2k}™1.$ A 1963 girth conjecture of Erdós, implies that $Ω(n^{1+1/k})$ space is needed in the worst case for any real stretch strictly smaller than $2\textit{k}+1.$ The space requirement of our algorithm is, therefore, essentially optimal. The most impressive feature of our data structure is its $\textit{constant}$ query time, hence the name "oracle". Previously, data structures that used only $O(n^{1+1/k})$ space had a query time of $Ω(n^{1/k}).Our$ algorithms are extremely simple and easy to implement efficiently. They also provide faster constructions of sparse $\textit{spanners}$ of weighted graphs, and improved tree covers and distance labelings of weighted or unweighted graphs.
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 2005-01-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 52
Issue Number 1
Page Count 24
Starting Page 1
Ending Page 24

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Source: ACM Digital Library