Tighter Bounds and Optimal Algorithms for All Maximal α-gapped Repeats and Palindromes

Finding All Maximal α-gapped Repeats and Palindromes in Optimal Worst Case Time on Integer Alphabets

Paweł Gawrychowski, I. Tomohiro, Shunsuke Inenaga, Dominik Köppl, Florin Manea

研究成果: ジャーナルへの寄稿記事

7 引用 (Scopus)

抄録

An α-gapped repeat (α ≥ 1) in a word w is a factor uvu of w such that |uv| ≤ α|u|; the two occurrences of u are called arms of this α-gapped repeat. An α-gapped repeat is called maximal if its arms cannot be extended simultaneously with the same character to the right nor to the left. We show that the number of all maximal α-gapped repeats occurring in words of length n is upper bounded by 18αn. In the case of α-gapped palindromes, i.e., factors uvu with |uv|≤ α|u|, we show that the number of all maximal α-gapped palindromes occurring in words of length n is upper bounded by 28αn + 7n. Both upper bounds allow us to construct algorithms finding all maximal α-gapped repeats and/or all maximal α-gapped palindromes of a word of length n on an integer alphabet of size nO ( 1 ) in O(αn) time. The presented running times are optimal since there are words that have Θ(αn) maximal α-gapped repeats/palindromes.

元の言語英語
ページ(範囲)162-191
ページ数30
ジャーナルTheory of Computing Systems
62
発行部数1
DOI
出版物ステータス出版済み - 1 1 2018

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Palindrome
Optimal Algorithm
Integer
Upper bound

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Computational Theory and Mathematics

これを引用

Tighter Bounds and Optimal Algorithms for All Maximal α-gapped Repeats and Palindromes : Finding All Maximal α-gapped Repeats and Palindromes in Optimal Worst Case Time on Integer Alphabets. / Gawrychowski, Paweł; Tomohiro, I.; Inenaga, Shunsuke; Köppl, Dominik; Manea, Florin.

:: Theory of Computing Systems, 巻 62, 番号 1, 01.01.2018, p. 162-191.

研究成果: ジャーナルへの寄稿記事

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