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Efficient Algorithms for Counting Gapped Palindromes

Authors Andrei Popa, Alexandru Popa

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Andrei Popa
  • Department of Computer Science, University of Bucharest, Romania
Alexandru Popa
  • Department of Computer Science, University of Bucharest, Romania

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Andrei Popa and Alexandru Popa. Efficient Algorithms for Counting Gapped Palindromes. In 32nd Annual Symposium on Combinatorial Pattern Matching (CPM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 191, pp. 23:1-23:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021) https://doi.org/10.4230/LIPIcs.CPM.2021.23

Abstract

A gapped palindrome is a string uvu^{R}, where u^{R} represents the reverse of string u. In this paper we show three efficient algorithms for counting the occurrences of gapped palindromes in a given string S of length N. First, we present a solution in O(N) time for counting all gapped palindromes without additional constraints. Then, in the case where the length of v is constrained to be in an interval [g, G], we show an algorithm with running time O(N log N). Finally, we show an algorithm in O(N log² N) time for a more general case where we count gapped palindromes uvu^{R}, where u^{R} starts at position i with g(i) ≤ v ≤ G(i), for all positions i.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • pattern matching
  • gapped palindromes
  • suffix tree

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