On strictly output sensitive color frequency reporting
Erwin Glazenburg, Frank Staals

TL;DR
This paper introduces a new data structure for color frequency reporting in multi-dimensional spaces that is strictly output sensitive, near-optimal, and adaptable to higher dimensions, improving query efficiency for colored point sets.
Contribution
The paper presents a simple, space-efficient data structure with output-sensitive query times, proves a lower bound for the weighted case, and extends results to higher dimensions.
Findings
Achieves $O( ext{ns} ext{log}_s n)$ size and $O( ext{log} n + k ext{log}_s n)$ query time in 2D.
Proves a near-matching lower bound for the weighted version, indicating near-optimality.
Provides a space reduction transformation and an efficient algorithm for dominance queries with linear space.
Abstract
Given a set of colored points we wish to store such that, given some query region , we can efficiently report the colors of the points appearing in the query region, along with their frequencies. This is the \emph{color frequency reporting} problem. We study the case where query regions are axis-aligned boxes or dominance ranges. If contains colors, the main goal is to achieve ``strictly output sensitive'' query time . Firstly, we show that, for every , there exists a simple size data structure for points in that allows frequency reporting queries in time. Secondly, we give a lower bound for the weighted version of the problem in the arithmetic model of computation, proving that with space one can not achieve query times better than…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Complexity and Algorithms in Graphs · Digital Image Processing Techniques
