Fast Multiple Pattern Cartesian Tree Matching

TL;DR

This paper introduces efficient algorithms for multiple pattern Cartesian tree matching using novel fingerprinting methods, significantly improving speed over previous solutions, especially for longer patterns.

Contribution

The paper presents three practical algorithms based on Wu-Manber, Rabin-Karp, and Alpha Skip Search, utilizing new fingerprinting techniques for faster Cartesian tree matching.

Findings

Algorithms outperform previous methods as pattern length increases.

Wu-Manber based algorithm is up to 33 times faster.

New fingerprinting methods improve matching efficiency.

Abstract

Cartesian tree matching is the problem of finding all substrings in a given text which have the same Cartesian trees as that of a given pattern. In this paper, we deal with Cartesian tree matching for the case of multiple patterns. We present two fingerprinting methods, i.e., the parent-distance encoding and the binary encoding. By combining an efficient fingerprinting method and a conventional multiple string matching algorithm, we can efficiently solve multiple pattern Cartesian tree matching. We propose three practical algorithms for multiple pattern Cartesian tree matching based on the Wu-Manber algorithm, the Rabin-Karp algorithm, and the Alpha Skip Search algorithm, respectively. In the experiments we compare our solutions against the previous algorithm [18]. Our solutions run faster than the previous algorithm as the pattern lengths increase. Especially, our algorithm based on Wu-Manber runs up to 33 times faster.