An improved algorithm for computing all the best swap edges of a tree spanner

Open access
Date
2017Type
- Conference Paper
Abstract
A tree sigma-spanner of a positively real-weighted n-vertex and m-edge undirected graph G is a spanning tree T of G which approximately preserves (i.e., up to a multiplicative stretch factor sigma) distances in G. Tree spanners with provably good stretch factors find applications in communication networks, distributed systems, and network design. However, finding an optimal or even a good tree spanner is a very hard computational task. Thus, if one has to face a transient edge failure in T, the overall effort that has to be afforded to rebuild a new tree spanner (i.e., computational costs, set-up of new links, updating of the routing tables, etc.) can be rather prohibitive. To circumvent this drawback, an effective alternative is that of associating with each tree edge a best possible (in terms of resulting stretch) swap edge -- a well-established approach in the literature for several other tree topologies. Correspondingly, the problem of computing all the best swap edges of a tree spanner is a challenging algorithmic problem, since solving it efficiently means to exploit the structure of shortest paths not only in G, but also in all the scenarios in which an edge of T has failed. For this problem we provide a very efficient solution, running in O(n^2 log^4 n) time, which drastically improves (almost by a quadratic factor in n in dense graphs!) on the previous known best result. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000224716Publication status
publishedExternal links
Book title
28th International Symposium on Algorithms and Computation (ISAAC 2017)Journal / series
Leibniz International Proceedings in Informatics (LIPIcs)Volume
Pages / Article No.
Publisher
Schloss Dagstuhl – Leibniz-Zentrum für InformatikEvent
Subject
Transient edge failure; Swap algorithm; Tree spannerOrganisational unit
03340 - Widmayer, Peter / Widmayer, Peter
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