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# 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} }

- Published 1998 in Algorithmica
DOI:10.1007/PL00009223

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 nâ€¦Â CONTINUE READING

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