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A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs.

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Τίτλος: A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs.
Συγγραφείς: Klein, P. N., Subramanian, S.
Πηγή: Algorithmica; Nov1998, Vol. 22 Issue 3, p235-249, 15p
Περίληψη: In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter $\epsilon$ such that $0<\epsilon$ , our algorithm maintains approximate all-pairs shortest paths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to within a 1+ $\epsilon$ factor. The time bounds for both query and update for our algorithm is O( \epsilon -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. The time bound for the queries is worst case, while that for the additions is amortized. Our approximation algorithm is based upon a novel technique for approximately representing all-pairs shortest paths among a selected subset of the nodes by a sparse substitute graph. [ABSTRACT FROM AUTHOR]
Copyright of Algorithmica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Βάση Δεδομένων: Complementary Index
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  – Url: https://dx.doi.org/doi:10.1007/PL00009223
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  Data: Algorithmica; Nov1998, Vol. 22 Issue 3, p235-249, 15p
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  Data: In this paper we give a fully dynamic approximation scheme for maintaining all-pairs shortest paths in planar networks. Given an error parameter $\epsilon$ such that $0&lt;\epsilon$ , our algorithm maintains approximate all-pairs shortest paths in an undirected planar graph G with nonnegative edge lengths. The approximate paths are guaranteed to be accurate to within a 1+ $\epsilon$ factor. The time bounds for both query and update for our algorithm is O( \epsilon &lt;superscript&gt; -1&lt;/superscript&gt; n&lt;superscript&gt; 2/3&lt;/superscript&gt; log&lt;superscript&gt; 2&lt;/superscript&gt; n log D) , where n is the number of nodes in G and D is the sum of its edge lengths. The time bound for the queries is worst case, while that for the additions is amortized. Our approximation algorithm is based upon a novel technique for approximately representing all-pairs shortest paths among a selected subset of the nodes by a sparse substitute graph. [ABSTRACT FROM AUTHOR]
– Name: Abstract
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  Group: Ab
  Data: &lt;i&gt;Copyright of Algorithmica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder&#39;s express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.&lt;/i&gt; (Copyright applies to all Abstracts.)
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              Text: Nov1998
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              Y: 1998
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