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#### On-line and Dynamic Shortest Paths through Graph Decompositions (Preliminary Version)

##### MPS-Authors

##### Locator

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##### Fulltext (public)

MPI-I-94-112.pdf

(Any fulltext), 125KB

##### Supplementary Material (public)

There is no public supplementary material available

##### Citation

Djidjev, H., Pantziou, G. E., & Zaroliagis, C.(1994). *On-line
and Dynamic Shortest Paths through Graph Decompositions (Preliminary Version)* (MPI-I-94-112). Saarbrücken: Max-Planck-Institut
für Informatik.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0014-B50A-6

##### Abstract

We describe algorithms for finding shortest paths and distances in a
planar digraph which exploit the particular topology of the input graph.
We give both sequential and parallel algorithms that
work on a dynamic environment, where the cost of any edge
can be changed or the edge can be deleted.
For outerplanar digraphs, for instance, the data
structures can be updated after any such change in only $O(\log n)$
time, where $n$ is the number of vertices of the digraph.
The parallel algorithms presented here are the first known ones
for solving this problem. Our results can be extended to hold for
digraphs of genus $o(n)$.