Linear Time Distributed Swap Edge Algorithms

  • Ajoy K. Datta
  • Lawrence L. Larmore
  • Linda Pagli
  • Giuseppe Prencipe
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7878)


In this paper, we consider the all best swap edges problem in a distributed environment. We are given a 2-edge connected positively weighted network X, where all communication is routed through a rooted spanning tree T of X. If one tree edge \(e={\left\{ x,y \right\} }\) fails, the communication network will be disconnected. However, since X is 2-edge connected, communication can be restored by replacing e by non-tree edge e′, called a swap edge of e, whose ends lie in different components of T − e. Of all possible swap edges of e, we would like to choose the best, as defined by the application. The all best swap edges problem is to identify the best swap edge for every tree edge, so that in case of any edge failure, the best swap edge can be activated quickly. There are solutions to this problem for a number of cases in the literature. A major concern for all these solutions is to minimize the number of messages. However, especially in fault-transient environments, time is a crucial factor. In this paper we present a novel technique that addresses this problem from a time perspective; in fact, we present a distributed solution that works in linear time with respect to the height h of T for a number of different criteria, while retaining the optimal number of messages. To the best of our knowledge, all previous solutions solve the problem in O(h 2) time in the cases we consider.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bilò, D., Gualà, L., Proietti, G.: Finding best swap edges minimizing the routing cost of a spanning tree. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 138–149. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  2. 2.
    Gfeller, B., Santoro, N., Widmayer, P.: A distributed algorithm for finding all best swap edges of a minimum diameter spanning tree. IEEE Trans. on Dependable and Secure Comp. 8(1), 1–12 (2011)CrossRefGoogle Scholar
  3. 3.
    Nardelli, E., Proietti, G., Widmayer, P.: Swapping a failing edge of a single source shortest paths tree is good and fast. Algorithmica 35(1), 56–74 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Nardelli, E., Proietti, G., Widmayer, P.: Nearly linear time minimum spanning tree maintenance for transient node failures. Algorithmica 40(1), 119–132 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Salvo, A.D., Proietti, G.: Swapping a failing edge of a shortest paths tree by minimizing the stretch factor. Theoretical Computer Science 383(1), 23–33 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  6. 6.
    Das, S., Gfeller, B., Widmayer, P.: Computing best swaps in optimal tree spanners. In: Hong, S.-H., Nagamochi, H., Fukunaga, T. (eds.) ISAAC 2008. LNCS, vol. 5369, pp. 716–727. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  7. 7.
    Flocchini, P., Enriques, A.M., Pagli, L., Prencipe, G., Santoro, N.: Point-of-failure shortest-path rerouting: Computing the optimal swap edges distributively. IEICE Transactions 89-D(2), 700–708 (2006)Google Scholar
  8. 8.
    Flocchini, P., Pagli, A.M.E.L., Prencipe, G., Santoro, N.: Distributed minumum spanning tree maintenance for transient node failures. IEEE Trans. on Comp. 61(3), 408–414 (2012)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Flocchini, P., Pagli, L., Prencipe, G., Santoro, N., Widmayer, P.: Computing all the best swap edges distributively. J. Parallel Distrib. Comput. 68(7), 976–983 (2008)zbMATHCrossRefGoogle Scholar
  10. 10.
    Pagli, L., Prencipe, G.: Brief annoucement: Distributed swap edges computation for minimum routing cost spanning trees. In: Abdelzaher, T., Raynal, M., Santoro, N. (eds.) OPODIS 2009. LNCS, vol. 5923, pp. 365–371. Springer, Heidelberg (2009)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Ajoy K. Datta
    • 1
  • Lawrence L. Larmore
    • 1
  • Linda Pagli
    • 2
  • Giuseppe Prencipe
    • 2
  1. 1.Dept. of Comp. Sc.Univ. of NevadaUSA
  2. 2.Dipartimento di InformaticaUniversità di PisaItaly

Personalised recommendations