Cartesian trees and Lyndon trees

TL;DR

This paper explores the structural and algorithmic connections between Cartesian trees and Lyndon Trees, providing a unified approach to related data structures and efficient computation of word periodicities.

Contribution

It introduces a unified framework linking Cartesian trees and Lyndon Trees, enabling efficient algorithms for computing word runs and periodicities.

Findings

Unified presentation of Lyndon table and Next Nearest Smaller table

Efficient algorithms for computing maximal periodicities in words

Structural insights into the relation between Cartesian and Lyndon trees

Abstract

The article describes the structural and algorithmic relations between Cartesian trees and Lyndon Trees. This leads to a uniform presentation of the Lyndon table of a word corresponding to the Next Nearest Smaller table of a sequence of numbers. It shows how to efficiently compute runs, that is, maximal periodicities occurring in a word.