Document Open Access Logo

Shortest Undirected Paths in de Bruijn Graphs

Authors Wiktor Zuba , Oded Lachish , Solon P. Pissis

PDF

File

Thumbnail PDF
PDF
LIPIcs.CPM.2025.12.pdf
  • Filesize: 1.09 MB
  • 13 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Theory of computation → Pattern matching
Keywords
  • string algorithm
  • graph algorithm
  • de Bruijn graph
  • Eulerian graph

Metrics

  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    0
    PDF Downloads
    0
    Metadata Views

Abstract

Computing shortest directed paths in de Bruijn graphs is well studied and well understood. This is not the case for computing undirected paths, which is much more challenging algorithmically. In this paper, we present a general framework for computing shortest undirected paths in arbitrary de Bruijn graphs, that is, arbitrary subgraphs of the complete de Bruijn graph. We then present an application of our techniques for making any arbitrary order-k de Bruijn graph G(V,E) weakly connected by adding a set of edges of minimum total cost. This improves the running time of the recent (2-2/d)-approximation algorithm by Bernardini et al. [CPM 2024] from 𝒪(k|V|²) to 𝒪(k|V|log d) time, where d is the number of weakly connected components of graph G.

Cite As Get BibTex

Wiktor Zuba, Oded Lachish, and Solon P. Pissis. Shortest Undirected Paths in de Bruijn Graphs. In 36th Annual Symposium on Combinatorial Pattern Matching (CPM 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 331, pp. 12:1-12:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CPM.2025.12

Author Details

Wiktor Zuba
  • CWI, Amsterdam, The Netherlands
  • University of Warsaw, Poland
Oded Lachish
  • Birkbeck, University of London, UK
Solon P. Pissis
  • CWI, Amsterdam, The Netherlands
  • Vrije Universiteit, Amsterdam, The Netherlands

Funding

A research visit during which part of the presented ideas were conceived was funded by a Royal Society International Exchanges Award.
  • Zuba, Wiktor: Supported in part by the Netherlands Organisation for Scientific Research (NWO) through Gravitation-grant NETWORKS that has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034253.
  • Pissis, Solon P.: Supported in part by the PANGAIA and ALPACA projects that have received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreements No 872539 and 956229, respectively.

References

  1. Nidia Obscura Acosta, Veli Mäkinen, and Alexandru I. Tomescu. A safe and complete algorithm for metagenomic assembly. Algorithms Mol. Biol., 13(1):3:1-3:12, 2018. URL: https://doi.org/10.1186/S13015-018-0122-7.
  2. Michael A. Bender, Alex Conway, Martin Farach-Colton, William Kuszmaul, and Guido Tagliavini. Iceberg hashing: Optimizing many hash-table criteria at once. J. ACM, 70(6):40:1-40:51, 2023. URL: https://doi.org/10.1145/3625817.
  3. Giulia Bernardini, Huiping Chen, Gabriele Fici, Grigorios Loukides, and Solon P. Pissis. Reverse-safe text indexing. ACM J. Exp. Algorithmics, 26:1.10:1-1.10:26, 2021. URL: https://doi.org/10.1145/3461698.
  4. Giulia Bernardini, Huiping Chen, Inge Li Gørtz, Christoffer Krogh, Grigorios Loukides, Solon P. Pissis, Leen Stougie, and Michelle Sweering. Connecting de Bruijn Graphs. In Shunsuke Inenaga and Simon J. Puglisi, editors, 35th Annual Symposium on Combinatorial Pattern Matching (CPM 2024), volume 296 of Leibniz International Proceedings in Informatics (LIPIcs), pages 6:1-6:16, Dagstuhl, Germany, 2024. Schloss Dagstuhl - Leibniz-Zentrum für Informatik. URL: https://doi.org/10.4230/LIPIcs.CPM.2024.6.
  5. Giulia Bernardini, Huiping Chen, Grigorios Loukides, Solon P. Pissis, Leen Stougie, and Michelle Sweering. Making de Bruijn graphs Eulerian. In Hideo Bannai and Jan Holub, editors, 33rd Annual Symposium on Combinatorial Pattern Matching, CPM 2022, June 27-29, 2022, Prague, Czech Republic, volume 223 of LIPIcs, pages 12:1-12:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/LIPICS.CPM.2022.12.
  6. Giulia Bernardini, Chang Liu, Grigorios Loukides, Alberto Marchetti-Spaccamela, Solon P. Pissis, Leen Stougie, and Michelle Sweering. Missing value replacement in strings and applications. Data Min. Knowl. Discov., 39(2):12, 2025. URL: https://doi.org/10.1007/S10618-024-01074-3.
  7. Giulia Bernardini, Alberto Marchetti-Spaccamela, Solon P. Pissis, Leen Stougie, and Michelle Sweering. Constructing strings avoiding forbidden substrings. In Pawel Gawrychowski and Tatiana Starikovskaya, editors, 32nd Annual Symposium on Combinatorial Pattern Matching, CPM 2021, July 5-7, 2021, Wrocław, Poland, volume 191 of LIPIcs, pages 9:1-9:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2021. URL: https://doi.org/10.4230/LIPICS.CPM.2021.9.
  8. Otakar Borůvka. O jistém problému minimálním. Práce Moravské přírodovědecké společnosti, sv. III(spis 3):37-58, 1926. URL: https://dml.cz/handle/10338.dmlcz/500114.
  9. Massimo Cairo, Shahbaz Khan, Romeo Rizzi, Sebastian Schmidt, Alexandru I. Tomescu, and Elia C. Zirondelli. The hydrostructure: a universal framework for safe and complete algorithms for genome assembly, 2021. URL: https://arxiv.org/abs/2011.12635.
  10. Alessio Conte, Roberto Grossi, Grigorios Loukides, Nadia Pisanti, Solon P. Pissis, and Giulia Punzi. Beyond the BEST theorem: Fast assessment of eulerian trails. In Evripidis Bampis and Aris Pagourtzis, editors, Fundamentals of Computation Theory - 23rd International Symposium, FCT 2021, Athens, Greece, September 12-15, 2021, Proceedings, volume 12867 of Lecture Notes in Computer Science, pages 162-175. Springer, 2021. URL: https://doi.org/10.1007/978-3-030-86593-1_11.
  11. Martin Farach. Optimal suffix tree construction with large alphabets. In 38th Annual Symposium on Foundations of Computer Science, FOCS '97, Miami Beach, Florida, USA, October 19-22, 1997, pages 137-143, 1997. URL: https://doi.org/10.1109/SFCS.1997.646102.
  12. John Gallant, David Maier, and James A. Storer. On finding minimal length superstrings. J. Comput. Syst. Sci., 20(1):50-58, 1980. URL: https://doi.org/10.1016/0022-0000(80)90004-5.
  13. Subhash Khot. On the power of unique 2-prover 1-round games. In Proceedings of the 17th Annual IEEE Conference on Computational Complexity, Montréal, Québec, Canada, May 21-24, 2002, page 25. IEEE Computer Society, 2002. URL: https://doi.org/10.1109/CCC.2002.1004334.
  14. Donald E. Knuth, James H. Morris Jr., and Vaughan R. Pratt. Fast pattern matching in strings. SIAM J. Comput., 6(2):323-350, 1977. URL: https://doi.org/10.1137/0206024.
  15. Lawrence T. Kou, George Markowsky, and Leonard Berman. A fast algorithm for Steiner trees. Acta Informatica, 15:141-145, 1981. URL: https://doi.org/10.1007/BF00288961.
  16. Zhen Liu. Optimal routing in the de Bruijn networks. In 10th International Conference on Distributed Computing Systems (ICDCS 1990), May 28 - June 1, 1990, Paris, France, pages 537-544. IEEE Computer Society, 1990. URL: https://doi.org/10.1109/ICDCS.1990.89261.
  17. Paul Medvedev, Konstantinos Georgiou, Gene Myers, and Michael Brudno. Computability of models for sequence assembly. In 7th WABI, volume 4645 of Lecture Notes in Computer Science, pages 289-301. Springer, 2007. URL: https://doi.org/10.1007/978-3-540-74126-8_27.
  18. Paul Medvedev and Mihai Pop. What do Eulerian and Hamiltonian cycles have to do with genome assembly? PLOS Computational Biology, 17(5):1-5, May 2021. URL: https://doi.org/10.1371/journal.pcbi.1008928.
  19. Jason R. Miller, Sergey Koren, and Granger Sutton. Assembly algorithms for next-generation sequencing data. Genomics, 95(6):315-327, 2010. URL: https://doi.org/10.1016/j.ygeno.2010.03.001.
  20. Donald R. Morrison. PATRICIA - practical algorithm to retrieve information coded in alphanumeric. J. ACM, 15(4):514-534, 1968. URL: https://doi.org/10.1145/321479.321481.
  21. Pavel A. Pevzner, Haixu Tang, and Michael S. Waterman. An Eulerian path approach to DNA fragment assembly. Proc Natl Acad Sci, 98(17):9748-9753, 2001. URL: https://doi.org/10.1073/pnas.171285098.
  22. Robert C. Prim. Shortest connection networks and some generalizations. Bell System Technical Journal, 36:1389-1401, 1957. URL: https://doi.org/10.1002/j.1538-7305.1957.tb01515.x.
  23. Sebastian Schmidt, Shahbaz Khan, Jarno N Alanko, Giulio E Pibiri, and Alexandru I Tomescu. Matchtigs: minimum plain text representation of k-mer sets. Genome Biology, 24(1):136, 2023. URL: https://doi.org/10.1186/s13059-023-02968-z.
  24. Alexandru I. Tomescu and Paul Medvedev. Safe and complete contig assembly through omnitigs. J. Comput. Biol., 24(6):590-602, 2017. URL: https://doi.org/10.1089/CMB.2016.0141.
  25. Peter Weiner. Linear pattern matching algorithms. In 14th Annual Symposium on Switching and Automata Theory, Iowa City, Iowa, USA, October 15-17, 1973, pages 1-11. IEEE Computer Society, 1973. URL: https://doi.org/10.1109/SWAT.1973.13.
Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2025 Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact