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Polynomial Time Algorithms for Edge-Connectivity Augmentation of Hamiltonian Paths

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Algorithms and Computation (ISAAC 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2223))

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Abstract

Given a graph G of n vertices and m edges, and given a spanning subgraph H of G, the problem of finding a minimum weight set of edges of G, denoted as Aug2(H,G), to be added to H to make it 2-edge connected, is known to be NP-hard. In this paper, we present polynomial time effcient algorithms for solving the special case of this classic augmentation problem in which the subgraph H is a Hamiltonian path of G. More precisely, we show that if G is unweighted, then Aug2(H,G) can be computed in O(m) time and space, while if G is non-negatively weighted, then Aug2(H,G) can be comp uted in O(m+n log n) time and O(m) space. These results have an interesting application for solving a survivability problem on communication networks.

This work has been partially supported by the CNR-Agenzia 2000 Program, under Grants No. CNRC00CAB8 and CNRG003EF8, and by the Research Project REACTION, partially funded by the Italian Ministry of University.

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Author information

Authors and Affiliations

  1. Istituto di Analisi dei Sistemi ed Informatica, CNR, Viale Manzoni 30, 00185, Roma, Italy

    Anna Galluccio

  2. Dipartimento di Matematica Pura ed Applicata, Universitá dell’Aquila, Via Vetoio, 67010, L’Aquila, Italy

    Guido Proietti

Authors
  1. Anna Galluccio
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  2. Guido Proietti
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Editor information

Editors and Affiliations

  1. Basser Department of Computer Science, University of Sydney, Madsen Building F09, 2006, Sydney, NSW, Australia

    Peter Eades

  2. Department of Computer Science, University of Canterbury, Private Bag 4800, Christchurch, New Zealand

    Tadao Takaoka

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© 2001 Springer-Verlag Berlin Heidelberg

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Galluccio, A., Proietti, G. (2001). Polynomial Time Algorithms for Edge-Connectivity Augmentation of Hamiltonian Paths. In: Eades, P., Takaoka, T. (eds) Algorithms and Computation. ISAAC 2001. Lecture Notes in Computer Science, vol 2223. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45678-3_30

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  • DOI: https://doi.org/10.1007/3-540-45678-3_30

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42985-2

  • Online ISBN: 978-3-540-45678-0

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