Eulertigs: Minimum Plain Text Representation of k-mer Sets Without Repetitions in Linear Time

Authors Sebastian Schmidt , Jarno N. Alanko

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Sebastian Schmidt
  • University of Helsinki, Finland
Jarno N. Alanko
  • University of Helsinki, Finland

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Sebastian Schmidt and Jarno N. Alanko. Eulertigs: Minimum Plain Text Representation of k-mer Sets Without Repetitions in Linear Time. In 22nd International Workshop on Algorithms in Bioinformatics (WABI 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 242, pp. 2:1-2:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)


A fundamental operation in computational genomics is to reduce the input sequences to their constituent k-mers. For maximum performance of downstream applications it is important to store the k-mers in small space, while keeping the representation easy and efficient to use (i.e. without k-mer repetitions and in plain text). Recently, heuristics were presented to compute a near-minimum such representation. We present an algorithm to compute a minimum representation in optimal (linear) time and use it to evaluate the existing heuristics. For that, we present a formalisation of arc-centric bidirected de Bruijn graphs and carefully prove that it accurately models the k-mer spectrum of the input. Our algorithm first constructs the de Bruijn graph in linear time in the length of the input strings (for a fixed-size alphabet). Then it uses a Eulerian-cycle-based algorithm to compute the minimum representation, in time linear in the size of the output.

Subject Classification

ACM Subject Classification
  • Applied computing → Computational biology
  • Theory of computation → Data compression
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Data structures design and analysis
  • Spectrum preserving string sets
  • Eulerian cycle
  • Suffix tree
  • Bidirected arc-centric de Bruijn graph
  • k-mer based methods


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