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- W2964194267 abstract "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 * binom{k+ceil[log n]}{k} * 2^k k^2 log n), where k is the treewidth of the graph. For every epsilon>0, this bound is n^{1+epsilon}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 algorithm of Cabello and Knauer (Comp. Geom., 2009) in the regime of non-constant treewidth can be improved by revisiting the analysis of orthogonal range searching, improving bounds of the form log^d n to binom{d+ceil[log n]}{d}, as originally observed by Monier (J. Alg. 1980). We also investigate the parameterization by vertex cover number. (Less)" @default.
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- W2964194267 date "2019-02-06" @default.
- W2964194267 modified "2023-10-18" @default.
- W2964194267 title "Multivariate Analysis of Orthogonal Range Searching and Graph Distances" @default.
- W2964194267 doi "https://doi.org/10.4230/lipics.ipec.2018.4" @default.
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