Cross-Document Pattern Matching

TL;DR

This paper introduces a new cross-document string matching problem, providing efficient linear-space solutions with minimal dependence on pattern size, and also improves the weighted level ancestor problem.

Contribution

It defines the cross-document string matching problem and offers novel linear-space algorithms with near-constant query times, advancing string matching techniques.

Findings

Efficient linear-space algorithms for cross-document string matching.

Query times are independent or weakly dependent on pattern size.

Improved solution to the weighted level ancestor problem.

Abstract

We study a new variant of the string matching problem called cross-document string matching, which is the problem of indexing a collection of documents to support an efficient search for a pattern in a selected document, where the pattern itself is a substring of another document. Several variants of this problem are considered, and efficient linear-space solutions are proposed with query time bounds that either do not depend at all on the pattern size or depend on it in a very limited way (doubly logarithmic). As a side result, we propose an improved solution to the weighted level ancestor problem.