Linear Time Inference of Strings from Cover Arrays using a Binary Alphabet

TL;DR

This paper introduces a linear-time algorithm for reconstructing strings from cover arrays over a binary alphabet, leveraging combinatorial properties and relations with border arrays.

Contribution

It presents the first linear-time method to infer strings from cover arrays using only a two-letter alphabet, improving efficiency and minimal alphabet size.

Findings

Algorithm reconstructs strings in linear time

Works over a binary alphabet

Utilizes combinatorial properties of cover arrays

Abstract

Covers being one of the most popular form of regularities in strings, have drawn much attention over time. In this paper, we focus on the problem of linear time inference of strings from cover arrays using the least sized alphabet possible. We present an algorithm that can reconstruct a string $x$ over a two-letter alphabet whenever a valid cover array $C$ is given as an input. This algorithm uses several interesting combinatorial properties of cover arrays and an interesting relation between border array and cover array to achieve this. Our algorithm runs in linear time.