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

@article{Klein1998AFD,
title={A Fully Dynamic Approximation Scheme for Shortest Paths in Planar Graphs},
author={Philip N. Klein and Sairam Subramanian},
journal={Algorithmica},
year={1998},
volume={22},
pages={235-249}
}
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… CONTINUE READING
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