LIPIcs.STACS.2009.1825.pdf
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Reverse Engineering Prefix Tables
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26th International Symposium on Theoretical Aspects of Computer Science (STACS 2009)
Series: Leibniz International Proceedings in Informatics (LIPIcs)
Conference: Symposium on Theoretical Aspects of Computer Science (STACS) - License:
Creative Commons Attribution-NoDerivs 3.0 Unported license
- Publication Date: 2009-02-19
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Julien Clement, Maxime Crochemore, and Giuseppina Rindone. Reverse Engineering Prefix Tables. In 26th International Symposium on Theoretical Aspects of Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 3, pp. 289-300, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
https://doi.org/10.4230/LIPIcs.STACS.2009.1825
https://doi.org/10.4230/LIPIcs.STACS.2009.1825
Abstract
The Prefix table of a string reports for each position the maximal length of its prefixes starting here. The Prefix table and its dual Suffix table are basic tools used in the design of the most efficient string-matching and pattern extraction algorithms. These tables can be computed in linear time independently of the alphabet size.
We give an algorithmic characterisation of a Prefix table (it can be adapted to a Suffix table). Namely, the algorithm tests if an integer table of size $n$ is the Prefix table of some word and, if successful, it constructs the lexicographically smallest string having it as a Prefix table. We show that the alphabet of the string can be bounded to $\log_2 n$ letters. The overall algorithm runs in $O(n)$ time.
Keywords
- Design and analysis of algorithms
- Algorithms on strings
- Pattern matching
- String matching
- Combinatorics on words
- Prefix table
- Suffix table
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