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Multivariate Analysis of Orthogonal Range Searching and Graph Distances

2019
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International Symposium on Parameterized and Exact Computation
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We show that the eccentricities, diameter, radius, and Wiener index of an undirected n-vertex graph with nonnegative edge lengths can be computed in time O(n · k+ log n k · 2 k k 2 log n), where k is the treewidth of the graph. For every > 0, this bound is n 1+ exp O(k), which matches a hardness result of Abboud, Vassilevska Williams, and Wang (SODA 2015) and closes an open problem in the multivariate analysis of polynomial-time computation. To this end, we show that the analysis of an

doi:10.4230/lipics.ipec.2018.4
dblp:conf/iwpec/BringmannHM18
fatcat:xx3ermqaqfho7d7k2ndpmcvydm