Joker de Bruijn: Covering κ-Mers using joker characters

Yaron Orenstein, Yun William Yu, Bonnie Berger

Research output: Contribution to journalArticlepeer-review


Sequence libraries that cover all k-mers enable universal and unbiased measurements of nucleotide and peptide binding. The shortest sequence to cover all k-mers is a de Bruijn sequence of length . Researchers would like to increase k to measure interactions at greater detail, but face a challenging problem: the number of k-mers grows exponentially in k, while the space on the experimental device is limited. In this study, we introduce a novel advance to shrink k-mer library sizes by using joker characters, which represent all characters in the alphabet. Theoretically, the use of joker characters can reduce the library size tremendously, but it should be limited as the introduced degeneracy lowers the statistical robustness of measurements. In this work, we consider the problem of generating a minimum-length sequence that covers a given set of k-mers using joker characters. The number and positions of the joker characters are provided as input. We first prove that the problem is NP-hard. We then present the first solution to the problem, which is based on two algorithmic innovations: (1) a greedy heuristic and (2) an integer linear programming (ILP) formulation. We first run the heuristic to find a good feasible solution, and then run an ILP solver to improve it. We ran our algorithm on DNA and amino acid alphabets to cover all k-mers for different values of k and k-mer multiplicity. Results demonstrate that it produces sequences that are very close to the theoretical lower bound.

Original languageEnglish
Pages (from-to)1171-1178
Number of pages8
JournalJournal of Computational Biology
Issue number11
StatePublished - 1 Nov 2018


  • de Bruijn sequence
  • microarray library design
  • peptide arrays
  • protein binding
  • protein binding microarrays

ASJC Scopus subject areas

  • Modeling and Simulation
  • Molecular Biology
  • Genetics
  • Computational Mathematics
  • Computational Theory and Mathematics


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