The Anti-Lexicographic SUS-Anchor: An Empirically Optimal Selection Scheme

[2606.01190] The Anti-Lexicographic SUS-Anchor: An Empirically Optimal Selection Scheme Skip to main content Search Submit Donate Log in Computer Science > Data Structures and Algorithms arXiv:2606.01190 (cs) [Submitted on 31 May 2026 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: The Anti-Lexicographic SUS-Anchor: An Empirically Optimal Selection Scheme Authors: Ragnar Groot Koerkamp View PDF HTML (experimental) Abstract: In recent years, there has been a renewed interest in the search for low density minimizer schemes. These schemes take a window of $w$ consecutive $k$-mers, and sample one of them: the smallest under some specific order. Schemes such as the mod-minimizer provide a low density (fraction of sampled $k$-mers) when $k \gg w$, while schemes such as the greedy minimizer work well for explicit small parameters roughly in the regime $k \leq 2w$, for $k$ and $w$ up to $15$ or so. When $k < \log_\sigma w$ is very small, minimizer schemes cannot do well, and more general sampling schemes are needed that can be richer than just comparing $k$-mers. Bidirectional-string anchors (bd-anchors) form one such scheme. Inspired by bd-anchors, we introduce the smallest unique substring or SUS-anchor: Given a window, this considers all suffixes that do not occur as a substring elsewhere in the window. It then samples the start position of the smallest suffix according to the new anti-lexicographic order that minimizes the first character and maximizes the remaining characters. We give a linear-time and $O(w)$ space streaming algorithm to compute all SUS-anchors of a string. For alphabet size $\sigma=4$ and $k=1$, the parameter-free anti-lexicographic SUS-anchor empirically has density $<1\%$ away from the density lower bound and is at least $4\times$ closer to the lower bound than all other tested schemes. For alphabet size $\sigma=2$, the density is at most $10\%$ above the lower bound, which still improves $2\times$ to $3\times$ the overhead of the random minimizer and is consistently better than the greedy minimizer. Likewise, the anti-lexicographic minimizer performs better than all other schemes apart from the greedy minimizer. Comments: 15 pages; 1 figure; updated to match the WABI 2026 version that compares against additional minimizer schemes; see also this https URL Subjects: Data Structures and Algorithms (cs.DS) Cite as: arXiv:2606.01190 [cs.DS] (or arXiv:2606.01190v3 [cs.DS] for this version) https://doi.org/10.48550/arXiv.2606.01190 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.4230/LIPIcs.WABI.2026.22 Focus to learn more DOI(s) linking to related resources Submission history From: Ragnar Groot Koerkamp [ view email ] [v1] Sun, 31 May 2026 12:11:49 UTC (595 KB) [v2] Tue, 2 Jun 2026 07:13:57 UTC (595 KB) [v3] Thu, 27 Aug 2026 10:01:10 UTC (1,123 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Additional Features Audio Summary Current browse context: cs.DS < prev | next > new | recent | 2026-06 Change to browse by: cs References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

Related documents

• The Anti-Lexicographic SUS-Anchor: An Empirically Optimal Selection Scheme#677620
• The Art of the Probable: Literature and Probability#67132
• Problems in High-Dimensional Estimation and Large Language Models#643872
• Johannes V. Jensen Corpus#486302
• Support for Geometric Pooling#697481