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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Showing 1-10 of 17 references

Biconnected Components of Dynamic Planar Graphs," Proceedings of the 18th International Collo- qium on Automata, Languages, and Programming

  • Z. Galil, G. F. Italiano, Maintaining
  • 1991
Highly Influential
8 Excerpts

Parallel and Dynamic Graph Algorithms: A Com- bined Perspective,

  • S. Subramanian
  • Ph.d Thesis, Department of Computer Science,
  • 1994

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