| Shortest Paths Avoiding Forbidden Subpaths (2009) | |||||||||||||
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| 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.. @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 (STACS 2009)}, pages = {63--74}, series = {Leibniz International Proceedings in Informatics}, year = {2009}, volume = {3}, editor = {Susanne Albers and Jean-Yves Marion}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, Germany}, address = {Dagstuhl, Germany}, URL = {http://drops.dagstuhl.de/opus/volltexte/2009/1831}, URN = {urn:nbn:de:0030-drops-18318}, annote = {Keywords: Algorithms and data structures, Graph algorithms, Optical networks} } | |||||||||||||
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