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Palindromic Decompositions with Gaps and Errors

  • Michał Adamczyk
  • Mai Alzamel
  • Panagiotis Charalampopoulos
  • Costas S. Iliopoulos
  • Jakub RadoszewskiEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10304)

Abstract

Identifying palindromes in sequences has been an interesting line of research in combinatorics on words and also in computational biology, after the discovery of the relation of palindromes in the DNA sequence with the HIV virus. Efficient algorithms for the factorization of sequences into palindromes and maximal palindromes have been devised in recent years. We extend these studies by allowing gaps in decompositions and errors in palindromes, and also imposing a lower bound to the length of acceptable palindromes.

We first present an algorithm for obtaining a palindromic decomposition of a string of length n with the minimal total gap length in time \(\mathcal {O}(n \log {n} \cdot g)\) and space \(\mathcal {O}(n \cdot g)\), where g is the number of allowed gaps in the decomposition. We then consider a decomposition of the string in maximal \(\delta \)-palindromes (i.e. palindromes with \(\delta \) errors under the edit or Hamming distance) and g allowed gaps. We present an algorithm to obtain such a decomposition with the minimal total gap length in time \(\mathcal {O}(n \cdot (g+\delta ))\) and space \(\mathcal {O}(n\cdot g)\).

Keywords

Dynamic Programming Time Algorithm Edit Distance Edit Operation Length Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Michał Adamczyk
    • 1
  • Mai Alzamel
    • 2
  • Panagiotis Charalampopoulos
    • 2
  • Costas S. Iliopoulos
    • 2
  • Jakub Radoszewski
    • 1
    • 2
    Email author
  1. 1.Faculty of Mathematics, Informatics and MechanicsUniversity of WarsawWarsawPoland
  2. 2.Department of InformaticsKing’s College LondonLondonUK

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