Advertisement

Algorithmica

, Volume 35, Issue 1, pp 56–74 | Cite as

Swapping a Failing Edge of a Single Source Shortest Paths Tree Is Good and Fast

  •  Nardelli
  •  Proietti
  •  Widmayer

Abstract. Let G=(V,E) be a 2-edge connected, undirected and nonnegatively weighted graph, and let S(r) be a single source shortest paths tree (SPT) of G rooted at r ∈ V . Whenever an edge e in S(r) fails, we are interested in reconnecting the nodes now disconnected from the root by means of a single edge e' crossing the cut created by the removal of e . Such an edge e' is named a swap edge for e . Let S e/e' (r) be the swap tree (no longer an SPT, in general) obtained by swapping e with e' , and let S e be the set of all possible swap trees with respect to e . Let F be a function defined over S e that expresses some feature of a swap tree, such as the average length of a path from the root r to all the nodes below edge e , or the maximum length, or one of many others. A best swap edge for e with respect to F is a swap edge f such that F(S e/f (r)) is minimum.

In this paper we present efficient algorithms for the problem of finding a best swap edge, for each edge e of S(r) , with respect to several objectives. Our work is motivated by a scenario in which individual connections in a communication network suffer transient failures. As a consequence of an edge failure, the shortest paths to all the nodes below the failed edge might completely change, and it might be desirable to avoid an expensive switch to a new SPT, because the failure is only temporary. As an aside, what we get is not even far from a new SPT: our analysis shows that the trees obtained from the swapping have features very similar to those of the corresponding SPTs rebuilt from scratch.

Key words. Network survivability, Single source shortest paths tree, Swap algorithms. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer-Verlag New York Inc. 2003

Authors and Affiliations

  •  Nardelli
    • 1
  •  Proietti
    • 1
  •  Widmayer
    • 2
  1. 1.Dipartimento di Informatica, Università di L'Aquila, Via Vetoio, 67010 L'Aquila, Italy, and Istituto di Analisi dei Sistemi ed Informatica ``A. Ruberti'', CNR, Viale Manzoni 30, 00185 Roma, Italy. nardelli@di.univaq.it, proietti@di.univaq.it.IT
  2. 2.Institut für Theoretische Informatik, ETH Zentrum, CLW C 2, Clausiusstrasse 49, 8092 Zürich, Switzerland. widmayer@inf.ethz.ch.CH

Personalised recommendations