English

Approximate Range Counting Revisited

Computational Geometry 2017-03-22 v3 Data Structures and Algorithms

Abstract

We study range-searching for colored objects, where one has to count (approximately) the number of colors present in a query range. The problems studied mostly involve orthogonal range-searching in two and three dimensions, and the dual setting of rectangle stabbing by points. We present optimal and near-optimal solutions for these problems. Most of the results are obtained via reductions to the approximate uncolored version, and improved data-structures for them. An additional contribution of this work is the introduction of nested shallow cuttings.

Keywords

Cite

@article{arxiv.1512.01713,
  title  = {Approximate Range Counting Revisited},
  author = {Saladi Rahul},
  journal= {arXiv preprint arXiv:1512.01713},
  year   = {2017}
}

Comments

A preliminary version of this paper has been accepted at SoCG 2017

R2 v1 2026-06-22T12:02:21.866Z