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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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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.

Cite AsGet BibTex

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

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.

Subject Classification

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

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