Paper Info
Title
Multivariate Analysis of Orthogonal Range Searching and Graph Distances
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 . (k + ([log n])(k) . 2(k) log n), where k is linear in the treewidth of the graph. For every epsilon > 0, this bound is n(1+epsilon)expO(k), which matches a hardness result of Abboud et al. (in: Proceedings of the Twenty-Seventh Annual ACM-SIAM Symposium on Discrete Algorithms, 2016. https://doi.org/10.1137/1.9781611974331.ch28) 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 (Comput Geom 42:815-824, 2009. https://doi.org/10.1016/j.comgeo.2009.02.001) 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 (6 + d([log n]) . 2, as originally observed by Monier (J Algorithms 1:60-74, 1980. https://doi.org/10.1016/0196-6774(80)90005-X). We also investigate the parameterization by vertex cover number.
Year
DOI
Venue
2020
10.1007/s00453-020-00680-z
ALGORITHMICA
Keywords
DocType
Volume
Diameter,Radius,Wiener index,Orthogonal range searching,Treewidth,Vertex cover number
Journal
82.0
Issue
ISSN
Citations 
SP8
0178-4617
0
PageRank 
References 
Authors
0.34
0
3
Name
Order
Citations
PageRank
Karl Bringmann142730.13
Thore Husfeldt273340.87
Måns Magnusson3162.47