# Color spanning Localized query

## TL;DR

This paper introduces efficient algorithms for pre-processing colored point sets to quickly identify the smallest color-spanning geometric object containing a query point, covering various shapes like intervals, squares, rectangles, triangles, and circles.

## Contribution

It presents novel algorithms for fast query processing of smallest color-spanning objects of multiple geometric types in a colored point set.

## Key findings

- Algorithms achieve efficient query times for various shapes.
- Pre-processing enables quick identification of smallest color-spanning objects.
- Applicable to multiple geometric shapes including intervals, squares, rectangles, triangles, and circles.

## Abstract

Let P be a set of n points and each of the points is colored with one of the k possible colors. We present efficient algorithms to pre-process P such that for a given query point q, we can quickly identify the smallest color spanning object of the desired type containing q. In this paper, we focus on (i) intervals, (ii) axis-parallel square, (iii) axis-parallel rectangle, (iv) equilateral triangle of fixed orientation and (v) circle, as our desired type of objects.