The Longest Run Subsequence Problem

Authors Sven Schrinner , Manish Goel , Michael Wulfert, Philipp Spohr , Korbinian Schneeberger , Gunnar W. Klau

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Sven Schrinner
  • Algorithmic Bioinformatics, Heinrich Heine University Düsseldorf, Germany
Manish Goel
  • Max Planck Institute for Plant Breeding Research, Cologne, Germany
Michael Wulfert
  • Algorithmic Bioinformatics, Heinrich Heine University Düsseldorf, Germany
Philipp Spohr
  • Algorithmic Bioinformatics, Heinrich Heine University Düsseldorf, Germany
Korbinian Schneeberger
  • Max Planck Institute for Plant Breeding Research, Cologne, Germany
  • Cluster of Excellence on Plant Sciences (CEPLAS), Heinrich Heine University Düsseldorf, Germany
  • Faculty of Biology, LMU Munich, Planegg-Martinsried, Germany
Gunnar W. Klau
  • Algorithmic Bioinformatics, Heinrich Heine University Düsseldorf, Germany
  • Cluster of Excellence on Plant Sciences (CEPLAS), Heinrich Heine University Düsseldorf, Germany

Cite AsGet BibTex

Sven Schrinner, Manish Goel, Michael Wulfert, Philipp Spohr, Korbinian Schneeberger, and Gunnar W. Klau. The Longest Run Subsequence Problem. In 20th International Workshop on Algorithms in Bioinformatics (WABI 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 172, pp. 6:1-6:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Genome assembly is one of the most important problems in computational genomics. Here, we suggest addressing the scaffolding phase, in which contigs need to be linked and ordered to obtain larger pseudo-chromosomes, by means of a second incomplete assembly of a related species. The idea is to use alignments of binned regions in one contig to find the most homologous contig in the other assembly. We show that ordering the contigs of the other assembly can be expressed by a new string problem, the longest run subsequence problem (LRS). We show that LRS is NP-hard and present reduction rules and two algorithmic approaches that, together, are able to solve large instances of LRS to provable optimality. In particular, they can solve realistic instances resulting from partial Arabidopsis thaliana assemblies in short computation time. Our source code and all data used in the experiments are freely available.

Subject Classification

ACM Subject Classification
  • Theory of computation → Dynamic programming
  • Mathematics of computing → Combinatorial optimization
  • Applied computing → Computational genomics
  • alignments
  • assembly
  • string algorithm
  • longest subsequence


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