tree ρ-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 ρ) 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(n2 log4 n) time, which drastically improves (almost by a quadratic factor in n in dense graphs!) on the previous known best result.
An improved algorithm for computing all the best swap edges of a tree spanner / Bilò, Davide; Colella, Feliciano; Gualà, Luciano; Leucci, Stefano; Proietti, Guido. - 92:(2017). (Intervento presentato al convegno 28th International Symposium on Algorithms and Computation, ISAAC 2017 tenutosi a tha nel 2017) [10.4230/LIPIcs.ISAAC.2017.14].
An improved algorithm for computing all the best swap edges of a tree spanner
Bilò, Davide;
2017-01-01
Abstract
tree ρ-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 ρ) 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(n2 log4 n) time, which drastically improves (almost by a quadratic factor in n in dense graphs!) on the previous known best result.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.