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Author Frederickson, Greg N.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1991
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword NP-completeness ♦ All pairs shortest paths ♦ Approximation algorithm ♦ Compact routing table ♦ Graph embedding ♦ Outerplanar graph ♦ Planar graph ♦ Succinct encoding
Abstract An algorithm is presented for generating a succinct encoding of all pairs shortest path information in a directed planar graph $\textit{G}$ with real-valued edge costs but no negative cycles. The algorithm runs in $\textit{O}(\textit{pn})$ time, where $\textit{n}$ is the number of vertices in $\textit{G},$ and $\textit{p}$ is the minimum cardinality of a subset of the faces that cover all vertices, taken over all planar embeddings of $\textit{G}.$ The algorithm is based on a decomposition of the graph into $\textit{O}(\textit{pn})$ outerplanar subgraphs satisfying certain separator properties. Linear-time algorithms are presented for various subproblems including that of finding an appropriate embedding of $\textit{G}$ and a corresponding face-on-vertex covering of cardinality $\textit{O}(\textit{p}),$ and of generating all pairs shortest path information in a directed outerplannar graph.
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 1991-01-03
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 38
Issue Number 1
Page Count 43
Starting Page 162
Ending Page 204


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Source: ACM Digital Library