Asymptotically Optimal Representation of Palindromic Structure

TL;DR

This paper presents an asymptotically optimal data structure for representing the Manacher array of a string, enabling constant-time access and leveraging palindrome properties for efficient compressed text indexing.

Contribution

It introduces a novel, compact representation of the Manacher array that is asymptotically optimal and supports constant-time queries, advancing palindrome-based text indexing methods.

Findings

Supports constant-time access to the Manacher array

Achieves asymptotic optimality in representation size

Highlights structural properties of palindromes for algorithmic use

Abstract

We introduce an asymptotically optimal representation of the Manacher array of a string that supports constant-time access. The approach relies on the combinatorial properties of palindromes, yielding a compact yet efficient structure. This work fits within the broader study of compressed text indexing and highlights structural aspects of palindromic substrings that may inspire further algorithmic applications.