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Author Demetrescu, Camil ♦ Italiano, Giuseppe F.
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 Dynamic graph algorithms ♦ Transitive closure
Abstract We present an algorithm for directed acyclic graphs that breaks through the $O(n^{2})$ barrier on the single-operation complexity of fully dynamic transitive closure, where $\textit{n}$ is the number of edges in the graph. We can answer queries in $O(n^{ε})$ worst-case time and perform updates in $O(n^{ω(1,ε,1)™ε}+n^{1+ε})$ worst-case time, for any ε∈[0,1], where ω(1,ε,1) is the exponent of the multiplication of an $\textit{n}$ × $n^{ε}$ matrix by an $n^{ε}$ × $\textit{n}$ matrix. The current best bounds on ω(1,ε,1) imply an $O(n^{0.575})$ query time and an $O(n^{1.575})$ update time in the worst case. Our subquadratic algorithm is randomized, and has one-sided error. As an application of this result, we show how to solve single-source reachability in $O(n^{1.575})$ time per update and constant time per query.
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 2005-03-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 52
Issue Number 2
Page Count 10
Starting Page 147
Ending Page 156


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Source: ACM Digital Library