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Replacement Paths and k Simple Shortest Paths in Unweighted Directed Graphs

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Book cover Automata, Languages and Programming (ICALP 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3580))

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Abstract

Let G=(V,E) be a directed graph and let P be a shortest path from s to t in G. In the replacement paths problem we are required to find, for every edge e on P, a shortest path from s to t in G that avoids e. We present the first non-trivial algorithm for computing replacement paths in unweighted directed graphs (and in graphs with small integer weights). Our algorithm is Monte-Carlo and its running time is \({\tilde O}(m\sqrt{n})\). Using the improved algorithm for the replacement paths problem we get an improved algorithm for finding the ksimple shortest paths between two given vertices.

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Authors and Affiliations

  1. School of Computer Science, Tel Aviv University, Tel Aviv, 69978, Israel

    Liam Roditty & Uri Zwick

Authors
  1. Liam Roditty
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  2. Uri Zwick
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Editor information

Editors and Affiliations

  1. CITI / Departamento de Informática, Universidade Nova de Lisboa, Portugal

    Luís Caires

  2. Dipartimento di Informatica, Sistemi e Produzione, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Roma, Italy

    Giuseppe F. Italiano

  3. Departamento de Informatica, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Luís Monteiro

  4. Ecole Polytechnique, Rue de Saclay, 91128, Palaiseau Cedex, France

    Catuscia Palamidessi

  5. Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, NY 10027, New York, USA

    Moti Yung

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© 2005 Springer-Verlag Berlin Heidelberg

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Roditty, L., Zwick, U. (2005). Replacement Paths and k Simple Shortest Paths in Unweighted Directed Graphs. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_21

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  • DOI: https://doi.org/10.1007/11523468_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-27580-0

  • Online ISBN: 978-3-540-31691-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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