## Improved Algorithms for Dynamic Shortest Paths (1996)

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Venue: | Algorithmica |

Citations: | 15 - 3 self |

### BibTeX

@ARTICLE{Djidjev96improvedalgorithms,

author = {Hristo N. Djidjev and Grammati E. Pantziou and Christos D. Zaroliagis},

title = {Improved Algorithms for Dynamic Shortest Paths},

journal = {Algorithmica},

year = {1996},

volume = {28},

pages = {2000}

}

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### Abstract

We describe algorithms for finding shortest paths and distances in outerplanar and planar digraphs that exploit the particular topology of the input graph. An important feature of our algorithms is that they can work in a dynamic environment, where the cost of any edge can be changed or the edge can be deleted. In the case of outerplanar digraphs, our data structures can be updated after any such change in only logarithmic time and a distance query is answered also in logarithmic time. In the case of planar digraphs, we give an interesting trade-off between preprocessing, query and update times depending on the value of a certain topological parameter of the graph. Our results can be extended to n-vertex digraphs of genus O(n 1\Gamma" ) for any " ? 0. Keywords: Shortest path, dynamic algorithm, planar digraph, outerplanar digraph. This work was partially supported by the NSF grant No. CCR-9409191 and by the EU ESPRIT LTR Project No. 20244 (ALCOM-IT). 1 Introduction 1.1 The prob...