Fast Set Intersection and Two Patterns Matching

TL;DR

This paper introduces a new problem called fast set intersection, providing efficient preprocessing methods for set intersection queries, and applies it to improve solutions for 2D substring indexing and document listing for two patterns.

Contribution

It proposes the fast set intersection problem and offers new solutions for related pattern matching and indexing problems via reduction techniques.

Findings

Efficient algorithms for fast set intersection.

Improved solutions for 2D substring indexing.

Enhanced document listing for two patterns.

Abstract

In this paper we present a new problem, the fast set intersection problem, which is to preprocess a collection of sets in order to efficiently report the intersection of any two sets in the collection. In addition we suggest new solutions for the two-dimensional substring indexing problem and the document listing problem for two patterns by reduction to the fast set intersection problem.