{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/an-optimal-algorithm-for-strict-circular","title":"An Optimal Algorithm for Strict Circular Seriation","arxiv_id":"2106.05944","date":"2021-06-10","proceeding":null,"authors":["Santiago Armstrong","Cristóbal Guzmán","Carlos A. Sing-Long"],"abstract":"We study the problem of circular seriation, where we are given a matrix of pairwise dissimilarities between $n$ objects, and the goal is to find a {\\em circular order} of the objects in a manner that is consistent with their dissimilarity. This problem is a generalization of the classical {\\em linear seriation} problem where the goal is to find a {\\em linear order}, and for which optimal ${\\cal O}(n^2)$ algorithms are known. Our contributions can be summarized as follows. First, we introduce {\\em circular Robinson matrices} as the natural class of dissimilarity matrices for the circular seriation problem. Second, for the case of {\\em strict circular Robinson dissimilarity matrices} we provide an optimal ${\\cal O}(n^2)$ algorithm for the circular seriation problem. Finally, we propose a statistical model to analyze the well-posedness of the circular seriation problem for large $n$. In particular, we establish ${\\cal O}(\\log(n)/n)$ rates on the distance between any circular ordering found by solving the circular seriation problem to the underlying order of the model, in the Kendall-tau metric.","url_abs":"https://arxiv.org/abs/2106.05944v1","url_pdf":"https://arxiv.org/pdf/2106.05944v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"an-optimal-algorithm-for-strict-circular","repo_url":"https://github.com/stgoa/recursiveseriation","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}