Color-spanning localized query

Abstract

Let P be a set of n points, where each point is colored with one of the k possible colors. We present efficient algorithms to preprocess 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.