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DOI: 10.4230/LIPIcs.STACS.2009.1831
URN: urn:nbn:de:0030-drops-18318
URL: https://drops.dagstuhl.de/opus/volltexte/2009/1831/
Ahmed, Mustaq ; Lubiw, Anna
Shortest Paths Avoiding Forbidden Subpaths
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Abstract
In this paper we study a variant of the shortest path problem in graphs: given a weighted graph $G$ and vertices $s$ and $t$, and given a set $X$ of forbidden paths in $G$, find a shortest $s$-$t$ path $P$ such that no path in $X$ is a subpath of $P$. Path $P$ is allowed to repeat vertices and edges. We call each path in $X$ an \emph{exception}, and our desired path a \emph{shortest exception avoiding path}. We formulate a new version of the problem where the algorithm has no a priori knowledge of $X$, and finds out about an exception $x \in X$ only when a path containing $x$ fails. This situation arises in computing shortest paths in optical networks. We give an algorithm that finds a shortest exception avoiding path in time polynomial in $|G|$ and $|X|$. The main idea is to run Dijkstra's algorithm incrementally after replicating vertices when an exception is discovered.
BibTeX - Entry
@InProceedings{ahmed_et_al:LIPIcs:2009:1831,
author = {Mustaq Ahmed and Anna Lubiw},
title = {{Shortest Paths Avoiding Forbidden Subpaths}},
booktitle = {26th International Symposium on Theoretical Aspects of Computer Science},
pages = {63--74},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-09-5},
ISSN = {1868-8969},
year = {2009},
volume = {3},
editor = {Susanne Albers and Jean-Yves Marion},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2009/1831},
URN = {urn:nbn:de:0030-drops-18318},
doi = {10.4230/LIPIcs.STACS.2009.1831},
annote = {Keywords: Algorithms and data structures, Graph algorithms, Optical networks}
}
| Keywords: | Algorithms and data structures, Graph algorithms, Optical networks | |
| Seminar: | 26th International Symposium on Theoretical Aspects of Computer Science | |
| Issue date: | 2009 | |
| Date of publication: | 19.02.2009 |
