Fault-Tolerant Approximate Shortest-Path Trees [article]

Davide Bilò and Luciano Gualà and Stefano Leucci and Guido Proietti
2016 arXiv   pre-print
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
more » ... e 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 n/ε^2) 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 n) 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.
arXiv:1407.0637v2 fatcat:nkpgrjyjsfhilbftisz5rycvqm