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Semi-dynamic shortest paths and breadth-first search in digraphs

  • Algorithms I
  • Conference paper
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STACS 97 (STACS 1997)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1200))

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Abstract

We show how to maintain a shortest path tree of a general directed graph G with unit edge weights and n vertices, during a sequence of edge deletions or a sequence of edge insertions, in O(n) amortized time per operation using linear space. Distance queries can be answered in constant time, while shortest path queries can be answered in time linear in the length of the retrieved path. These results are extended to the case of integer edge weights in [1,C], with a bound of O(Cn) amortized time per operation.

We also show how to maintain a breadth-first search tree of a directed graph G in an incremental or a decremental setting in O(n) amortized time per operation using linear space.

Work partially supported by EC ESPRIT Long Term Research Project ALCOM-IT under contract no. 20244, and by Progetto Finalizzato Trasporti 2 (PFT 2) of the Italian National Research Council (CNR).

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Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Università di Roma “La Sapienza”, via Salaria 113, I-00198, Roma, Italy

    Paolo Giulio Franciosa, Daniele Frigioni & Roberto Giaccio

  2. Dipartimento di Matematica Pura ed Applicata, Università di L'Aquila, via Vetoio, I-67010, Coppito, AQ, Italy

    Daniele Frigioni

Authors
  1. Paolo Giulio Franciosa
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  2. Daniele Frigioni
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  3. Roberto Giaccio
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Editor information

Rüdiger Reischuk Michel Morvan

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© 1997 Springer-Verlag Berlin Heidelberg

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Franciosa, P.G., Frigioni, D., Giaccio, R. (1997). Semi-dynamic shortest paths and breadth-first search in digraphs. In: Reischuk, R., Morvan, M. (eds) STACS 97. STACS 1997. Lecture Notes in Computer Science, vol 1200. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0023446

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  • DOI: https://doi.org/10.1007/BFb0023446

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-62616-9

  • Online ISBN: 978-3-540-68342-1

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