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Efficiently Finding All Maximal alpha-gapped Repeats
Abstract
For alpha >=1, an alpha-gapped repeat in a word w is a factor uvu of w such that |uv| <= alpha * |u|; the two occurrences of a factor u in such a repeat are called arms. Such a repeat is called maximal if its arms cannot be extended simultaneously with the same symbol to the right nor to the left. We show that the number of all maximal alpha-gapped repeats occurring in words of length n is upper bounded by 18 * alpha * n, allowing us to construct an algorithm finding all maximal alpha-gapped repeats of a word on an integer alphabet of size n^{O}(1)} in {O}(alpha * n) time. This result is optimal as there are words that have Theta(alpha * n) maximal alpha-gapped repeats. Our techniques can be extended to get comparable results in the case of alpha-gapped palindromes, i.e., factors uvu^{T} with |uv| <= alpha |u|.
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“Gawrychowski and Manea (2015) defined algorithms that find the longest α -gapped palindromes and repeats in O ( αn ) time; these algorithms do not compute the set of all α -gapped palindromes or repeats, but just the ones with the longest arms.”
From Longest Gapped Repeats and Palindromes (2017) · cites this paper as Gawrychowski and Manea (2015)
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Longest Gapped Repeats and Palindromes
Dumitran, M., Gawrychowski, P., & Manea, F. (2017) · Discrete Mathematics & Theoretical Computer Science · doi:10.23638/dmtcs-19-4-4 · Cited by 11
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Metadata
- Authors
- Gawrychowski, P., I, T., Inenaga, S., Köppl, D., & Manea, F.
- Venue
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Publisher
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Published
- 2016
- References
- 0
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- Gawrychowski, P., I, T., Inenaga, S., Köppl, D., & Manea, F. (2016). Efficiently Finding All Maximal alpha-gapped Repeats. Schloss Dagstuhl – Leibniz-Zentrum für Informatik. https://doi.org/10.4230/lipics.stacs.2016.39
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