Λεπτομέρειες βιβλιογραφικής εγγραφής
| 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] |
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