Priority Range Trees
Michael T. Goodrich, Darren Strash

TL;DR
The paper introduces a priority range tree data structure that efficiently handles orthogonal range reporting queries on prioritized points, enabling fast retrieval of points based on rank and weight in logarithmic time.
Contribution
It presents a novel data structure, the priority range tree, optimized for prioritized range queries, with specific time complexities and space bounds for three- and four-sided queries.
Findings
Supports fast reporting of points with rank at least a threshold
Efficiently reports top-ranked points within a range
Achieves optimal space complexity for three-sided queries
Abstract
We describe a data structure, called a priority range tree, which accommodates fast orthogonal range reporting queries on prioritized points. Let be a set of points in the plane, where each point in is assigned a weight that is polynomial in , and define the rank of to be . Then the priority range tree can be used to report all points in a three- or four-sided query range with rank at least in time , and report highest-rank points in in time , where , is the smallest weight of any point reported, and is the output size. All times assume the standard RAM model of computation. If the query range of interest is three sided, then the priority range tree occupies space, otherwise space is used to…
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Taxonomy
TopicsData Management and Algorithms · Computational Geometry and Mesh Generation · Algorithms and Data Compression
