Multivariate Analysis of Orthogonal Range Searching and Graph Distances
(2019) 13th International Symposium on Parameterized and Exact Computation (IPEC 2018). In LIPIcs 115. p.1-13- 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... (More)
- 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)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/b966bcba-fa40-4a84-8fa7-7179f00d8073
- author
- Bringmann, Karl ; Husfeldt, Thore ^{LU} and Magnusson, Måns
- organization
- publishing date
- 2019-02-06
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- host publication
- 13th International Symposium on Parameterized and Exact Computation, IPEC 2018 : August 20-24, 2018, Helsinki, Finland - August 20-24, 2018, Helsinki, Finland
- series title
- LIPIcs
- editor
- Paul, Christophe ; Philipczuk, Michał ; and
- volume
- 115
- article number
- 4
- pages
- 13 pages
- publisher
- Schloss Dagstuhl - Leibniz-Zentrum für Informatik
- conference name
- 13th International Symposium on Parameterized and Exact Computation (IPEC 2018).
- conference location
- Helsinki, Finland
- conference dates
- 2018-08-20 - 2018-08-24
- ISBN
- 978-3-95977-084-2
- DOI
- 10.4230/LIPIcs.IPEC.2018.4
- project
- Algebraic Graph Algorithms
- language
- English
- LU publication?
- yes
- id
- b966bcba-fa40-4a84-8fa7-7179f00d8073
- date added to LUP
- 2019-02-27 09:35:17
- date last changed
- 2019-02-27 11:31:13
@inproceedings{b966bcba-fa40-4a84-8fa7-7179f00d8073, 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.}, author = {Bringmann, Karl and Husfeldt, Thore and Magnusson, Måns}, booktitle = {13th International Symposium on Parameterized and Exact Computation, IPEC 2018 : August 20-24, 2018, Helsinki, Finland}, editor = {Paul, Christophe and Philipczuk, Michał}, isbn = {978-3-95977-084-2}, language = {eng}, month = {02}, pages = {1--13}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum für Informatik}, series = {LIPIcs}, title = {Multivariate Analysis of Orthogonal Range Searching and Graph Distances}, url = {http://dx.doi.org/10.4230/LIPIcs.IPEC.2018.4}, doi = {10.4230/LIPIcs.IPEC.2018.4}, volume = {115}, year = {2019}, }