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Path-Fault-Tolerant Approximate Shortest-Path Trees

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Structural Information and Communication Complexity (SIROCCO 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9439))

Abstract

Let G = (V,E) be an n-nodes non-negatively real-weighted undirected graph. In this paper we show how to enrich a single-source shortest-path tree (SPT) of G with a sparse set of auxiliary edges selected from E, in order to create a structure which tolerates effectively a path failure in the SPT. This consists of a simultaneous fault of a set F of at most f adjacent edges along a shortest path emanating from the source, and it is recognized as one of the most frequent disruption in an SPT. We show that, for any integer parameter k ≥ 1, it is possible to provide a very sparse (i.e., of size O(kn·f 1 + 1/k)) auxiliary structure that carefully approximates (i.e., within a stretch factor of (2k − 1)(2|F| + 1)) the true shortest paths from the source during the lifetime of the failure. Moreover, we show that our construction can be further refined to get a stretch factor of 3 and a size of O(n logn) for the special case f = 2, and that it can be converted into a very efficient approximate-distance sensitivity oracle, that allows to quickly (even in optimal time, if k = 1) reconstruct the shortest paths (w.r.t. our structure) from the source after a path failure, thus permitting to perform promptly the needed rerouting operations. Our structure compares favorably with previous known solutions, as we discuss in the paper, and moreover it is also very effective in practice, as we assess through a large set of experiments.

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Authors and Affiliations

  1. Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università degli Studi dell’Aquila, Via Vetoio, I-67100, L’Aquila, Italy

    Annalisa D’Andrea, Mattia D’Emidio, Daniele Frigioni, Stefano Leucci & Guido Proietti

  2. Istituto di Analisi dei Sistemi ed Informatica “Antonio Ruberti”, Consiglio Nazionale delle Ricerche, Via dei Taurini 19, I-00185, Roma, Italy

    Guido Proietti

Authors
  1. Annalisa D’Andrea
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  2. Mattia D’Emidio
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  3. Daniele Frigioni
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  4. Stefano Leucci
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  5. Guido Proietti
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Corresponding author

Correspondence to Annalisa D’Andrea .

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Editors and Affiliations

  1. Dept of Mathematics and Comp Science, Paderborn University, Paderborn, Nordrhein-Westfalen, Germany

    Christian Scheideler

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D’Andrea, A., D’Emidio, M., Frigioni, D., Leucci, S., Proietti, G. (2015). Path-Fault-Tolerant Approximate Shortest-Path Trees. In: Scheideler, C. (eds) Structural Information and Communication Complexity. SIROCCO 2015. Lecture Notes in Computer Science(), vol 9439. Springer, Cham. https://doi.org/10.1007/978-3-319-25258-2_16

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  • DOI: https://doi.org/10.1007/978-3-319-25258-2_16

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