eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-06-08
28:1
28:15
10.4230/LIPIcs.SoCG.2018.28
article
On the Complexity of Closest Pair via Polar-Pair of Point-Sets
David, Roee
C. S., Karthik
Laekhanukit, Bundit
Every graph G can be represented by a collection of equi-radii spheres in a d-dimensional metric Delta such that there is an edge uv in G if and only if the spheres corresponding to u and v intersect. The smallest integer d such that G can be represented by a collection of spheres (all of the same radius) in Delta is called the sphericity of G, and if the collection of spheres are non-overlapping, then the value d is called the contact-dimension of G. In this paper, we study the sphericity and contact dimension of the complete bipartite graph K_{n,n} in various L^p-metrics and consequently connect the complexity of the monochromatic closest pair and bichromatic closest pair problems.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol099-socg2018/LIPIcs.SoCG.2018.28/LIPIcs.SoCG.2018.28.pdf
Contact dimension
Sphericity
Closest Pair
Fine-Grained Complexity