Algorithms and Data Structures
Volume 709 of the series Lecture Notes in Computer Science pp 442451
A fully dynamic approximation scheme for allpairs shortest paths in planar graphs
 Philip N. KleinAffiliated withDepartment of Computer Science, Brown University
 , Sairam SubramanianAffiliated withDepartment of Computer Science, Brown University
Abstract
In this paper we give a fully dynamic approximation scheme for maintaining allpairs shortest paths in planar networks. Given an error parameter ε such that 0<ε≤1, our algorithm maintains approximate allpairs shortestpaths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to within a (1+ε)factor. The time bounds for both query and update for our algorithm wis O(ε ^{−1} n ^{2/3} log^{2} n log D), where n is the number of nodes in G and D is the sum of its edge lengths.
Our approximation algorithm is based upon a novel technique for approximately representing allpairs shortest paths among a selected subset of the nodes by a sparse substitute graph.
 Title
 A fully dynamic approximation scheme for allpairs shortest paths in planar graphs
 Book Title
 Algorithms and Data Structures
 Book Subtitle
 Third Workshop, WADS '93 Montréal, Canada, August 11–13, 1993 Proceedings
 Pages
 pp 442451
 Copyright
 1993
 DOI
 10.1007/3540571558_269
 Print ISBN
 9783540571551
 Online ISBN
 9783540479185
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 709
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
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 Editors
 Authors

 Philip N. Klein ^{(1)}
 Sairam Subramanian ^{(1)}
 Author Affiliations

 1. Department of Computer Science, Brown University, 02912, Providence, R. I., USA
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