When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2009.1831
URN: urn:nbn:de:0030-drops-18318
URL: http://drops.dagstuhl.de/opus/volltexte/2009/1831/
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### 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},