Answering Spatial Multiple-Set Intersection Queries Using 2-3 Cuckoo Hash-Filters

TL;DR

This paper introduces a new data structure called 2-3 cuckoo hash-filters that significantly improves the efficiency of answering spatial multiple-set intersection queries, especially in GIS applications, by leveraging word-RAM model operations.

Contribution

The paper presents a novel data structure and algorithm that reduce the expected time complexity for spatial multiple-set intersection queries in the word-RAM model.

Findings

Achieves O(n(log w)/w + kt) expected time complexity

Improves upon previous solutions in asymptotic performance

Applicable to spatial join queries in GIS using space-filling curves

Abstract

We show how to answer spatial multiple-set intersection queries in O(n(log w)/w + kt) expected time, where n is the total size of the t sets involved in the query, w is the number of bits in a memory word, k is the output size, and c is any fixed constant. This improves the asymptotic performance over previous solutions and is based on an interesting data structure, known as 2-3 cuckoo hash-filters. Our results apply in the word-RAM model (or practical RAM model), which allows for constant-time bit-parallel operations, such as bitwise AND, OR, NOT, and MSB (most-significant 1-bit), as exist in modern CPUs and GPUs. Our solutions apply to any multiple-set intersection queries in spatial data sets that can be reduced to one-dimensional range queries, such as spatial join queries for one-dimensional points or sets of points stored along space-filling curves, which are used in GIS applications.