Closest-Pair Queries and Minimum-Weight Queries are Equivalent for Squares
Abstract
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 $R \cap S$. In the range minimum weight problem, we want to report the minimum weight of any point in the set $R \cap S$. We show that these two query problems are equivalent for query ranges that are squares, for data structures having $\Omega(\log n)$ query times. As a result, we obtain new data structures for range closest pair queries with squares.
- Publication:
-
arXiv e-prints
- Pub Date:
- October 2020
- DOI:
- 10.48550/arXiv.2010.06463
- arXiv:
- arXiv:2010.06463
- Bibcode:
- 2020arXiv201006463K
- Keywords:
-
- Computer Science - Computational Geometry