The resiliency of a network is its ability to remain effectively functioning also when any of its nodes or links fails. However, to reduce operational and set-up costs, a network should be small in size, and this conflicts with the requirement of being resilient. In this paper we address this trade-off for the prominent case of the broadcasting routing scheme, and we build efficient (i.e., sparse and fast) fault-tolerant approximate shortest-path trees, for both the edge and vertex single-failure case. In particular, for an n-vertex non-negatively weighted graph, and for any constant ε>0, we design two structures of size O(n log n/ε2 which guarantee (1+ε)-stretched paths from the selected source also in the presence of an edge/vertex failure. This favorably compares with the currently best known solutions, which are for the edge-failure case of size O(n) and stretch factor 3, and for the vertex-failure case of size O(n logn) and stretch factor 3. Moreover, we also focus on the unweighted case, and we prove that an ordinary (α,β)-spanner can be slightly augmented in order to build efficient fault-tolerant approximate breadth-first-search trees. © 2014 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Bilò, D., Gualà, L., Leucci, S., & Proietti, G. (2014). Fault-tolerant approximate shortest-path trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8737 LNCS, pp. 137–148). Springer Verlag. https://doi.org/10.1007/978-3-662-44777-2_12
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