15  Background on low density minimizers

TBA

• the quest for lower density
• recent progress (Pellow et al., 2023; Groot Koerkamp & Pibiri, 2024; Alanko et al., 2025; Golan et al., 2025; Groot Koerkamp et al., 2025; Shur et al., 2026)
• see Ragnar’s thesis (Groot Koerkamp, 2025)
• practical impact of lower density: fewer queries, less space usage (e.g. in K2Rmini, Deacon, SSHash or KFC)

Alanko, J.N., Biagi, E., & Puglisi, S.J. (2025) Finimizers: Variable-length bounded-frequency minimizers for k-mer sets. IEEE Transactions on Computational Biology and Bioinformatics, 22, 899–910.

Golan, S., Tziony, I., Kraus, M., Orenstein, Y., & Shur, A. (2025) GreedyMini: Generating low-density DNA minimizers. Bioinformatics, 41, i275–i284.

Groot Koerkamp, R. (2025) Optimal throughput bioinformatics (PhD thesis). URL https://www.research-collection.ethz.ch/handle/20.500.11850/783091.

Groot Koerkamp, R., Liu, D., & Pibiri, G.E. (2025) The open-closed mod-minimizer algorithm. Algorithms for Molecular Biology, 20.

Groot Koerkamp, R. & Pibiri, G.E. (2024) The mod-minimizer: A Simple and Efficient Sampling Algorithm for Long k-mers. 24th international workshop on algorithms in bioinformatics (WABI 2024), vol. 312, Leibniz international proceedings in informatics (LIPIcs) (Pissis, S.P. & Sung, W.-K. eds). Dagstuhl, Germany: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, pp. 11:1–11:23.

Pellow, D., Pu, L., Ekim, B., Kotlar, L., Berger, B., Shamir, R., & Orenstein, Y. (2023) Efficient minimizer orders for large values of k using minimum decycling sets. Genome Research.

Shur, A., Tziony, I., & Orenstein, Y. (2026) 10-minimizers: A promising class of constant-space minimizers. bioRxiv.