# MPI-I-96-1-012

## A simple parallel algorithm for the single-source shortest path problem on planar diagraphs

### Träff, Jesper L. and Zaroliagis, Christos D.

**MPI-I-96-1-012**. June** **1996, 17 pages. | Status:** **available - back from printing | Next --> Entry | Previous <-- Entry

Abstract in LaTeX format:

We present a simple parallel algorithm for the {\em single-source shortest path problem} in {\em planar digraphs} with nonnegative real edge weights.

The algorithm runs on the EREW PRAM model of parallel computation in $O((n^{2\epsilon} + n^{1-\epsilon})\log n)$ time, performing

$O(n^{1+\epsilon}\log n)$ work for any $0<\epsilon<1/2$. The strength of the algorithm is its simplicity, making it easy to implement, and presumably 474 quite efficient in practice.

The algorithm improves upon the work of all previous algorithms.

The work can be further reduced to $O(n^{1+\epsilon})$, by plugging in a less practical, sequential planar shortest path

algorithm.

Our algorithm is based on a region decomposition of the input graph, and uses a well-known parallel implementation of Dijkstra's algorithm.

Acknowledgement:** **

References to related material:

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**URL to this document: **http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/1996-1-012

**BibTeX**
`@TECHREPORT{``TräffZaroliagis96``,`

` AUTHOR = {Tr{\"a}ff, Jesper L. and Zaroliagis, Christos D.},`

` TITLE = {A simple parallel algorithm for the single-source shortest path problem on planar diagraphs},`

` TYPE = {Research Report},`

` INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},`

` ADDRESS = {Im Stadtwald, D-66123 Saarbr{\"u}cken, Germany},`

` NUMBER = {MPI-I-96-1-012},`

` MONTH = {June},`

` YEAR = {1996},`

` ISSN = {0946-011X},`

`}`