Revisiting $O(n \log \log n)$ chaining for anchored edit distance

[2606.03929] Revisiting $O(n \log \log n)$ chaining for anchored edit distance Skip to main content Search Submit Donate Log in Computer Science > Data Structures and Algorithms arXiv:2606.03929 (cs) [Submitted on 2 Jun 2026 ( v1 ), last revised 27 Aug 2026 (this version, v2)] Title: Revisiting $O(n \log \log n)$ chaining for anchored edit distance Authors: Nicola Rizzo , Ragnar Groot Koerkamp View PDF HTML (experimental) Abstract: Colinear chaining is a classical heuristic for sequence alignment: it enables scalable genome comparison and is a main component of many state-of-the-art read mappers based on seed-chain-extend. The earliest $O(n \log \log n)$ and $O(n \log n)$ time algorithms by Eppstein et al. (J. ACM, 1992) chained $n$ fragments between two sequences $T$ and $Q$ while minimizing a gap cost based on the diagonal distance $\Delta_{\text{diag}}$ between consecutive fragments. They also forbid fragment overlaps, which are essential in current chaining formulations: in long-read mapping, overlaps improve sensitivity and avoid restrictions on the fragment class considered. Jain, Gibney, and Thankachan (J. Comput. Biol. 2022) recently combined a $\Delta_{\text{diag}} = |\Delta_T -\Delta_Q|$ overlap cost with the classic $L_\infty = \max(\Delta_T , \Delta_Q)$ gap cost that takes the maximum between the horizontal and vertical gap between the fragments and they proved that chaining under this cost model is equivalent to the anchored edit distance. We improve the existing $O(n \log^3 n)$-time algorithm for anchored edit distance to $O(n \log \log n)$ time in $O(n)$ space, by combining the gap-cost computation of Chao and Miller (Algorithmica, 1995) with the overlap-cost computation of Baker and Giancarlo (ESA, 1998). By developing llchain, a simpler $O(n \log n)$-time implementation of our method, we show how chaining algorithms that might have been recently overlooked by the bioinformatics community scale competitively to millions of fragments and large genomes. On average, llchain is $10\times$ faster than other methods on instances with $3\,000\,000$ anchors, and over $2.3\times$ faster on MEMs between HiFi reads and a reference human genome. Comments: 20 pages; 5 figures; updated to match WABI 2026 published version apart from rotated table Subjects: Data Structures and Algorithms (cs.DS) Cite as: arXiv:2606.03929 [cs.DS] (or arXiv:2606.03929v2 [cs.DS] for this version) https://doi.org/10.48550/arXiv.2606.03929 Focus to learn more arXiv-issued DOI via DataCite Related DOI : https://doi.org/10.4230/LIPIcs.WABI.2026.13 Focus to learn more DOI(s) linking to related resources Submission history From: Ragnar Groot Koerkamp [ view email ] [v1] Tue, 2 Jun 2026 17:18:53 UTC (340 KB) [v2] Thu, 27 Aug 2026 09:36:05 UTC (398 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)

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