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Finding All Maximal Perfect Haplotype Blocks in Linear Time

Authors Jarno Alanko , Hideo Bannai , Bastien Cazaux , Pierre Peterlongo , Jens Stoye

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Author Details

Jarno Alanko
  • Department of Computer Science, University of Helsinki, Finland
Hideo Bannai
  • Department of Informatics, Kyushu University, Japan
Bastien Cazaux
  • Department of Computer Science, University of Helsinki, Finland
Pierre Peterlongo
  • Univ. Rennes, Inria, CNRS, Irisa, France
Jens Stoye
  • Faculty of Technology and Center for Biotechnology (CeBiTec), Bielefeld University, Germany


We thank the organizers of DSB 2019 ( for giving us the opportunity to present earlier work in this area and start a discussion from which the present results originated. We would also like to thank Michel T. Henrichs for providing a script to convert VCF files to haplotype matrices and for assisting with the production of Figure 3.

Cite AsGet BibTex

Jarno Alanko, Hideo Bannai, Bastien Cazaux, Pierre Peterlongo, and Jens Stoye. Finding All Maximal Perfect Haplotype Blocks in Linear Time. In 19th International Workshop on Algorithms in Bioinformatics (WABI 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 143, pp. 8:1-8:9, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


Recent large-scale community sequencing efforts allow at an unprecedented level of detail the identification of genomic regions that show signatures of natural selection. Traditional methods for identifying such regions from individuals' haplotype data, however, require excessive computing times and therefore are not applicable to current datasets. In 2019, Cunha et al. (Proceedings of BSB 2019) suggested the maximal perfect haplotype block as a very simple combinatorial pattern, forming the basis of a new method to perform rapid genome-wide selection scans. The algorithm they presented for identifying these blocks, however, had a worst-case running time quadratic in the genome length. It was posed as an open problem whether an optimal, linear-time algorithm exists. In this paper we give two algorithms that achieve this time bound, one conceptually very simple one using suffix trees and a second one using the positional Burrows-Wheeler Transform, that is very efficient also in practice.

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
  • Applied computing → Bioinformatics
  • Mathematics of computing → Combinatorial algorithms
  • Applied computing → Computational genomics
  • Population genomics
  • selection coefficient
  • haplotype block
  • positional Burrows-Wheeler Transform


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