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The Maximum Duo-Preservation String Mapping Problem with Bounded Alphabet

Authors Nicolas Boria , Laurent Gourvès, Vangelis Th. Paschos , Jérôme Monnot

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Author Details

Nicolas Boria
  • Université Paris-Dauphine, Université PSL, CNRS, LAMSADE, 75016, Paris, France
Laurent Gourvès
  • Université Paris-Dauphine, Université PSL, CNRS, LAMSADE, 75016, Paris, France
Vangelis Th. Paschos
  • Université Paris-Dauphine, Université PSL, CNRS, LAMSADE, 75016, Paris, France
Jérôme Monnot
  • Université Paris-Dauphine, Université PSL, CNRS, LAMSADE, 75016, Paris, France

Funding

  • Boria, Nicolas: Supported by Agence Nationale de la Recherche (ANR), project STAP ANR-17-CE23-0021.
  • Gourvès, Laurent: Supported by Agence Nationale de la Recherche (ANR), project THEMIS ANR-20-CE23-0018

Cite AsGet BibTex

Nicolas Boria, Laurent Gourvès, Vangelis Th. Paschos, and Jérôme Monnot. The Maximum Duo-Preservation String Mapping Problem with Bounded Alphabet. In 21st International Workshop on Algorithms in Bioinformatics (WABI 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 201, pp. 5:1-5:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/LIPIcs.WABI.2021.5

Abstract

Given two strings A and B such that B is a permutation of A, the max duo-preservation string mapping (MPSM) problem asks to find a mapping π between them so as to preserve a maximum number of duos. A duo is any pair of consecutive characters in a string and it is preserved by π if its two consecutive characters in A are mapped to same two consecutive characters in B. This problem has received a growing attention in recent years, partly as an alternative way to produce approximation algorithms for its minimization counterpart, min common string partition, a widely studied problem due its applications in comparative genomics. Considering this favored field of application with short alphabet, it is surprising that MPSM^𝓁, the variant of MPSM with bounded alphabet, has received so little attention, with a single yet impressive work that provides a 2.67-approximation achieved in O(n) [Brubach, 2018], where n = |A| = |B|. Our work focuses on MPSM^𝓁, and our main contribution is the demonstration that this problem admits a Polynomial Time Approximation Scheme (PTAS) when 𝓁 = O(1). We also provide an alternate, somewhat simpler, proof of NP-hardness for this problem compared with the NP-hardness proof presented in [Haitao Jiang et al., 2012].

Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Dynamic programming
  • Theory of computation → Pattern matching
  • Theory of computation → Complexity classes
Keywords
  • Maximum-Duo Preservation String Mapping
  • Bounded alphabet
  • Polynomial Time Approximation Scheme

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