Shortest Paths Avoiding Forbidden Subpaths

Authors Mustaq Ahmed, Anna Lubiw



PDF
Thumbnail PDF

File

LIPIcs.STACS.2009.1831.pdf
  • Filesize: 206 kB
  • 12 pages

Document Identifiers

Author Details

Mustaq Ahmed
Anna Lubiw

Cite AsGet BibTex

Mustaq Ahmed and Anna Lubiw. Shortest Paths Avoiding Forbidden Subpaths. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 63-74, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.STACS.2009.1831

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.
Keywords
  • Algorithms and data structures
  • Graph algorithms
  • Optical networks

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail