Cartesian Forest Matching

TL;DR

This paper introduces Cartesian Forests, a generalization of Cartesian Trees for partially ordered sequences, along with algorithms that achieve average linear time complexity for exact and approximate matching, and explores their relation to Schr"oder Trees.

Contribution

It extends Cartesian Tree algorithms to Cartesian Forests, providing new matching algorithms and establishing a correspondence with Schr"oder Trees.

Findings

Algorithms for Cartesian Forest Matching run in average linear time.

Filters improve the efficiency of exact matching algorithms.

Cartesian Forests are equivalent to Schr"oder Trees.

Abstract

In this paper, we introduce the notion of Cartesian Forest, which generalizes Cartesian Trees, in order to deal with partially ordered sequences. We show that algorithms that solve both exact and approximate Cartesian Tree Matching can be adapted to solve Cartesian Forest Matching in average linear time. We adapt the notion of Cartesian Tree Signature to Cartesian Forests and show how filters can be used to experimentally improve the algorithm for the exact matching. We also show a one to one correspondence between Cartesian Forests and Schr\"oder Trees.