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Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences

Authors Mitsuru Funakoshi , Yuto Nakashima , Shunsuke Inenaga , Hideo Bannai , Masayuki Takeda , Ayumi Shinohara

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Subject Classification

ACM Subject Classification
  • Mathematics of computing → Combinatorial algorithms
Keywords
  • string algorithms
  • pattern matching
  • bit parallelism
  • subsequences
  • cadences

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Abstract

The equidistant subsequence pattern matching problem is considered. Given a pattern string P and a text string T, we say that P is an equidistant subsequence of T if P is a subsequence of the text such that consecutive symbols of P in the occurrence are equally spaced. We can consider the problem of equidistant subsequences as generalizations of (sub-)cadences. We give bit-parallel algorithms that yield o(n²) time algorithms for finding k-(sub-)cadences and equidistant subsequences. Furthermore, O(nlog² n) and O(nlog n) time algorithms, respectively for equidistant and Abelian equidistant matching for the case |P| = 3, are shown. The algorithms make use of a technique that was recently introduced which can efficiently compute convolutions with linear constraints.

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Mitsuru Funakoshi, Yuto Nakashima, Shunsuke Inenaga, Hideo Bannai, Masayuki Takeda, and Ayumi Shinohara. Detecting k-(Sub-)Cadences and Equidistant Subsequence Occurrences. In 31st Annual Symposium on Combinatorial Pattern Matching (CPM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 161, pp. 12:1-12:11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.CPM.2020.12

Author Details

Mitsuru Funakoshi
  • Department of Informatics, Kyushu University, Fukuoka, Japan
Yuto Nakashima
  • Department of Informatics, Kyushu University, Fukuoka, Japan
Shunsuke Inenaga
  • Department of Informatics, Kyushu University, Fukuoka, Japan
  • PRESTO, Japan Science and Technology Agency, Kawaguchi, Japan
Hideo Bannai
  • M&D Data Science Center, Tokyo Medical and Dental University, Tokyo, Japan
Masayuki Takeda
  • Department of Informatics, Kyushu University, Fukuoka, Japan
Ayumi Shinohara
  • Graduate School of Information Sciences, Tohoku University, Sendai, Japan

Funding

  • Funakoshi, Mitsuru: JSPS KAKENHI Grant Number JP20J21147.
  • Nakashima, Yuto: JSPS KAKENHI Grant Number JP18K18002.
  • Inenaga, Shunsuke: JSPS KAKENHI Grant Number JP17H01697, JST PRESTO Grant Number JPMJPR1922.
  • Bannai, Hideo: JSPS KAKENHI Grant Numbers JP16H02783, JP20H04141.
  • Takeda, Masayuki: JSPS KAKENHI Grant Number JP18H04098.
  • Shinohara, Ayumi: JSPS KAKENHI Grant Number JP15H05706.

References

  1. Amihood Amir, Alberto Apostolico, Travis Gagie, and Gad M. Landau. String cadences. Theoretical Computer Science, 698:4-8, 2017. Algorithms, Strings and Theoretical Approaches in the Big Data Era (In Honor of the 60th Birthday of Professor Raffaele Giancarlo). Google Scholar
  2. Robert S. Boyer and J. Strother Moore. A fast string searching algorithm. Commun. ACM, 20(10):762–772, 1977. Google Scholar
  3. Maxime Crochemore and Dominique Perrin. Two-way string-matching. J. ACM, 38(3):650–674, 1991. Google Scholar
  4. Simone Faro, Thierry Lecroq, Stefano Borzi, Simone Di Mauro, and Alessandro Maggio. The string matching algorithms research tool. In Proceedings of the Prague Stringology Conference 2016, Prague, Czech Republic, August 29-31, 2016, pages 99-111. Department of Theoretical Computer Science, Faculty of Information Technology, Czech Technical University in Prague, 2016. Google Scholar
  5. Mitsuru Funakoshi and Julian Pape-Lange. Non-rectangular convolutions and (sub-)cadences with three elements. In 37th International Symposium on Theoretical Aspects of Computer Science, STACS 2020, March 10-13, 2020, Montpellier, France, volume 154 of LIPIcs, pages 30:1-30:16. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2020. Google Scholar
  6. Zvi Galil and Joel Seiferas. Time-space-optimal string matching. Journal of Computer and System Sciences, 26(3):280-294, 1983. Google Scholar
  7. J. Gardelle. Cadences. Mathématiques et Sciences humaines, 9:31-38, 1964. Google Scholar
  8. R. Nigel Horspool. Practical fast searching in strings. Software: Practice and Experience, 10(6):501-506, 1980. Google Scholar
  9. Donald E. Knuth, James H. Morris Jr., and Vaughan R. Pratt. Fast pattern matching in strings. SIAM J. Comput., 6(2):323-350, 1977. Google Scholar
  10. M. Lothaire. Combinatorics on Words. Cambridge Mathematical Library. Cambridge University Press, 1997. Google Scholar
  11. Phillip Matier and Andrew Ross. Did Schwarzenegger drop 4-letter bomb in veto? San Francisco Chronicle, 2009. URL: http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2009/10/28/MNBN1ABKB8.DTL.
  12. Doron Witztum, Eliyahu Rips, and Yoav Rosenberg. Equidistant letter sequences in the book of genesis. Statistical Science, 9(3):429-438, 1994. Google Scholar
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