Sigma-local graphs

Authors:
Prosenjit Bose;Sébastien Collette;Stefan Langerman;Anil Maheshwari;Pat Morin;Michiel Smid
Affiliations:
School of Computer Science, Carleton University, Canada;Computer Science Department, Université Libre de Bruxelles, Belgium;Computer Science Department, Université Libre de Bruxelles, Belgium;School of Computer Science, Carleton University, Canada;School of Computer Science, Carleton University, Canada;School of Computer Science, Carleton University, Canada
Venue:
Journal of Discrete Algorithms
Year:
2010

Citing 12
Cited 1

An O(n log n) algorithm for the all-nearest-neighbors problem

Discrete & Computational Geometry
Solving query-retrieval problems by compacting Voronoi diagrams

STOC '90 Proceedings of the twenty-second annual ACM symposium on Theory of computing
Optimal parallel randomized algorithms for three-dimensional convex hulls and related problems

SIAM Journal on Computing
Classes of graphs which approximate the complete Euclidean graph

Discrete & Computational Geometry
Relative neighborhood graphs in three dimensions

Computational Geometry: Theory and Applications
The &ggr;-neighborhood graph

Computational Geometry: Theory and Applications
A decomposition of multidimensional point sets with applications to k-nearest-neighbors and n-body potential fields

Journal of the ACM (JACM)
Randomized algorithms

Randomized algorithms
Applying Parallel Computation Algorithms in the Design of Serial Algorithms

Journal of the ACM (JACM)
On the Spanning Ratio of Gabriel Graphs and beta-Skeletons

SIAM Journal on Discrete Mathematics
Algorithms for Reporting and Counting Geometric Intersections

IEEE Transactions on Computers
Local polyhedra and geometric graphs

Computational Geometry: Theory and Applications - Special issue on the 19th annual symposium on computational geometry - SoCG 2003

Locally-scaled spectral clustering using empty region graphs

Proceedings of the 18th ACM SIGKDD international conference on Knowledge discovery and data mining

Quantified Score

Hi-index	0.00

Visualization

Abstract

We introduce and analyze @s-local graphs, based on a definition of locality by Erickson [J. Erickson, Local polyhedra and geometric graphs, Computational Geometry: Theory and Applications 31 (1-2) (2005) 101-125]. We present two algorithms to construct such graphs, for any real number @s1 and any set S of n points. These algorithms run in time O(@s^dn+nlogn) for sets in R^d and O(nlog^3nloglogn+k) for sets in the plane, where k is the size of the output. For sets in the plane, algorithms to find the minimum or maximum @s such that the corresponding graph has properties such as connectivity, planarity, and no-isolated vertex are presented, with complexities in O(nlog^O^(^1^)n). These algorithms can also be used to efficiently construct the corresponding graphs.