Longest Gapped Repeats and Palindromes
A gapped repeat (respectively, palindrome) occurring in a word $w$ is a factor $uvu$ (respectively, $u^Rvu$) of $w$. In such a repeat (palindrome) $u$ is called the arm of the repeat (respectively, palindrome), while $v$ is called the gap. We show how to compute efficiently, for every position $i$ o...
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| Published in: | Discrete mathematics and theoretical computer science Vol. 19 no. 4, FCT '15; no. special issue FCT'15 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Discrete Mathematics & Theoretical Computer Science
13.10.2017
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| Subjects: | |
| ISSN: | 1365-8050, 1365-8050 |
| Online Access: | Get full text |
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| Summary: | A gapped repeat (respectively, palindrome) occurring in a word $w$ is a factor $uvu$ (respectively, $u^Rvu$) of $w$. In such a repeat (palindrome) $u$ is called the arm of the repeat (respectively, palindrome), while $v$ is called the gap. We show how to compute efficiently, for every position $i$ of the word $w$, the longest gapped repeat and palindrome occurring at that position, provided that the length of the gap is subject to various types of restrictions. That is, that for each position $i$ we compute the longest prefix $u$ of $w[i..n]$ such that $uv$ (respectively, $u^Rv$) is a suffix of $w[1..i-1]$ (defining thus a gapped repeat $uvu$ -- respectively, palindrome $u^Rvu$), and the length of $v$ is subject to the aforementioned restrictions.
Comment: This is an extension of the conference papers "Longest $\alpha$-Gapped Repeat and Palindrome", presented by the second and third authors at FCT 2015, and "Longest Gapped Repeats and Palindromes", presented by the first and third authors at MFCS 2015 |
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| ISSN: | 1365-8050 1365-8050 |
| DOI: | 10.23638/DMTCS-19-4-4 |