Dynamic 3-sided Planar Range Queries with Expected Doubly Logarithmic Time

TL;DR

This paper introduces new deterministic data structures for 3-sided range queries in 2D, achieving expected doubly logarithmic query times in both main and external memory models, considering various input distributions.

Contribution

It provides the first deterministic solutions for 3-sided range queries with expected doubly logarithmic time in RAM and I/O models across different input distributions.

Findings

Achieves expected doubly logarithmic query time

Provides solutions in both RAM and external memory models

Considers a variety of input distributions

Abstract

This work studies the problem of 2-dimensional searching for the 3-sided range query of the form $[a, b]\times (-\infty, c]$ in both main and external memory, by considering a variety of input distributions. We present three sets of solutions each of which examines the 3-sided problem in both RAM and I/O model respectively. The presented data structures are deterministic and the expectation is with respect to the input distribution.