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# Prefix Sorting DFAs: A Recursive Algorithm

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LIPIcs.ISAAC.2023.22.pdf
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## Acknowledgements

I thank Nicola Prezza for pointing out the paper [Sung{-}Hwan Kim et al., 2023].

## Cite As

Nicola Cotumaccio. Prefix Sorting DFAs: A Recursive Algorithm. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
https://doi.org/10.4230/LIPIcs.ISAAC.2023.22

## Abstract

In the past thirty years, numerous algorithms for building the suffix array of a string have been proposed. In 2021, the notion of suffix array was extended from strings to DFAs, and it was shown that the resulting data structure can be built in O(m² + n^{5/2}) time, where n is the number of states and m is the number of edges [SODA 2021]. Recently, algorithms running in O(mn) and O(n²log n) time have been described [CPM 2023]. In this paper, we improve the previous bounds by proposing an O(n²) recursive algorithm inspired by Farach’s algorithm for building a suffix tree [FOCS 1997]. To this end, we provide insight into the rich lexicographic and combinatorial structure of a graph, so contributing to the fascinating journey which might lead to solve the long-standing open problem of building the suffix tree of a graph.

## Subject Classification

##### ACM Subject Classification
• Theory of computation → Graph algorithms analysis
• Theory of computation → Pattern matching
##### Keywords
• Suffix Array
• Burrows-Wheeler Transform
• FM-index
• Recursive Algorithms
• Graph Theory
• Pattern Matching

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