Closest-Pair Queries and Minimum-Weight Queries are Equivalent for Squares

10/13/2020
by   Abrar Kazi, et al.
0

Let S be a set of n weighted points in the plane and let R be a query range in the plane. In the range closest pair problem, we want to report the closest pair in the set R ∩ S. In the range minimum weight problem, we want to report the minimum weight of any point in the set R ∩ S. We show that these two query problems are equivalent for query ranges that are squares, for data structures having Ω(log n) query times. As a result, we obtain new data structures for range closest pair queries with squares.

READ FULL TEXT

page 1

page 2

page 3

page 4

09/27/2018

Closest-Pair Queries in Fat Rectangles

In the range closest pair problem, we want to construct a data structure...
07/26/2018

Colored range closest-pair problem under general distance functions

The range closest-pair (RCP) problem is the range-search version of the ...
12/28/2017

New bounds for range closest-pair problems

Given a dataset S of points in R^2, the range closest-pair (RCP) problem...
04/30/2022

Chromatic k-Nearest Neighbor Queries

Let P be a set of n colored points. We develop efficient data structures...
11/19/2020

Verifying the Correctness of Analytic Query Results

Data outsourcing is a cost-effective solution for data owners to tackle ...
09/18/1998

Separation-Sensitive Collision Detection for Convex Objects

We develop a class of new kinetic data structures for collision detectio...
03/20/2013

Why Do We Need Foundations for Modelling Uncertainties?

Surely we want solid foundations. What kind of castle can we build on sa...