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Improved Purely Additive Fault-Tolerant Spanners

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Book cover Algorithms - ESA 2015

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9294))

Abstract

Let G be an unweighted n-node undirected graph. A β-additive spanner of G is a spanning subgraph H of G such that distances in H are stretched at most by an additive term β w.r.t. the corresponding distances in G. A natural research goal related with spanners is that of designing sparse spanners with low stretch.

In this paper, we focus on fault-tolerant additive spanners, namely additive spanners which are able to preserve their additive stretch even when one edge fails. We are able to improve all known such spanners, in terms of either sparsity or stretch. In particular, we consider the sparsest known spanners with stretch 6, 28, and 38, and reduce the stretch to 4, 10, and 14, respectively (while keeping the same sparsity).

Our results are based on two different constructions. On one hand, we show how to augment (by adding a small number of edges) a fault-tolerant additive sourcewise spanner (that approximately preserves distances only from a given set of source nodes) into one such spanner that preserves all pairwise distances. On the other hand, we show how to augment some known fault-tolerant additive spanners, based on clustering techniques. This way we decrease the additive stretch without any asymptotic increase in their size. We also obtain improved fault-tolerant additive spanners for the case of one vertex failure, and for the case of f edge failures.

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Authors and Affiliations

  1. Dipartimento di Scienze Umanistiche e Sociali, Università di Sassari, Sassari, Italy

    Davide Bilò

  2. IDSIA, University of Lugano, Lugano, Switzerland

    Fabrizio Grandoni

  3. Dipartimento di Ingegneria dell’Impresa, Università di Roma “Tor Vergata”, Rome, Italy

    Luciano Gualà

  4. DISIM, Università degli Studi dell’Aquila, L’Aquila, Italy

    Stefano Leucci & Guido Proietti

  5. Istituto di Analisi dei Sistemi ed Informatica, CNR, Roma, Italy

    Guido Proietti

Authors
  1. Davide Bilò
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  2. Fabrizio Grandoni
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  3. Luciano Gualà
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  4. Stefano Leucci
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  5. Guido Proietti
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Corresponding author

Correspondence to Davide Bilò .

Editor information

Editors and Affiliations

  1. University of Technology, Eindhoven, The Netherlands

    Nikhil Bansal

  2. Sapienza University of Rome, Rome, Italy

    Irene Finocchi

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Bilò, D., Grandoni, F., Gualà, L., Leucci, S., Proietti, G. (2015). Improved Purely Additive Fault-Tolerant Spanners. In: Bansal, N., Finocchi, I. (eds) Algorithms - ESA 2015. Lecture Notes in Computer Science(), vol 9294. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48350-3_15

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  • DOI: https://doi.org/10.1007/978-3-662-48350-3_15

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  • Print ISBN: 978-3-662-48349-7

  • Online ISBN: 978-3-662-48350-3

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