2018/07/03 by Davide Bilò, Bilò, Davide, Kleitos Papadopoulos +1
Computer Science · #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #cs.DS
paper · pdf · doi:10.48550/arxiv.1807.01260
The paper has been accepted for publication at the 29th International Symposium on Algorithms and Computation (ISAAC 2018). 12 pages, 3 figures
arxiv created 2018/10/02 · arxiv updated 2018/10/03
Given a 2-edge connected, unweighted, and undirected graph G with n vertices and m edges, a σ-tree spanner is a spanning tree T of G in which the ratio between the distance in T of any pair of vertices and the corresponding distance in G is upper bounded by σ. The minimum value of σ for which T is a σ-tree spanner of G is also called the \em stretch factor of T. We address the fault-tolerant scenario in which each edge e of a given tree spanner may temporarily fail and has to be replaced by a \em best swap edge, i.e. an edge that reconnects T-e at a minimum stretch factor. More precisely, we design an O(n2) time and space algorithm that computes a best swap edge of every tree edge. Previously, an O(n2 log4 n) time and O(n2+mlog2n) space algorithm was known for edge-weighted graphs [Bilò et al., ISAAC 2017]. Even if our improvements on both the time and space complexities are of a polylogarithmic factor, we stress the fact that the design of a o(n2) time and space algorithm would be considered a breakthrough.