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Author Eppstein, David ♦ Galil, Zvi ♦ Italiano, Giuseppe F. ♦ Nissenzweig, Amnon
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1997
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Dynamic graph algorithms ♦ Edge and vertex connectivity ♦ Minimum spanning trees
Abstract We provide data strutures that maintain a graph as edges are inserted and deleted, and keep track of the following properties with the following times: minimum spanning forests, graph connectivity, graph 2-edge connectivity, and bipartiteness in $time\textit{O}(\textit{n}1/2)$ per change; 3-edge connectivity, in time $\textit{O}(\textit{n}2/3)$ per change; 4-edge connectivity, in time $\textit{O}(\textit{n}α(\textit{n}))$ per change; $\textit{k}-edge$ connectivity for constant $\textit{k},$ in time $\textit{O}(\textit{n}log\textit{n})$ per change;2-vertex connectivity, and 3-vertex connectivity, in the $\textit{O}(\textit{n})$ per change; and 4-vertex connectivity, in time $\textit{O}(\textit{n}α(\textit{n}))$ per change. Further results speed up the insertion times to match the bounds of known partially dynamic algorithms.All our algorithms are based on a new technique that transforms an algorithm for sparse graphs into one that will work on any graph, which we call $\textit{sparsification.}$
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 1997-09-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 44
Issue Number 5
Page Count 28
Starting Page 669
Ending Page 696


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Source: ACM Digital Library