{"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/fast-and-simple-unrooted-dynamic-forests","title":"Fast and simple unrooted dynamic forests","arxiv_id":"2310.18036","date":"2023-10-27","proceeding":null,"authors":["Benjamin Aram Berendsohn"],"abstract":"A dynamic forest data structure maintains a forest (and associated data like edge weights) under edge insertions and deletions. Dynamic forests are widely used to solve online and offline graph problems. Well-known examples of dynamic forest data structures are link-cut trees [Sleator and Tarjan '83] and top trees [Alstrup, Holm, de Lichtenberg, and Thorup '05], both of which need O(log n) time per operation. While top trees are more flexible and arguably easier to use, link-cut trees are faster in practice [Tarjan and Werneck '10]. In this paper, we propose an alternative to link-cut trees. Our data structure is based on search trees on trees (STTs, also known as elimination trees) and an STT algorithm [Berendsohn and Kozma '22] based on the classical Splay trees [Sleator and Tarjan '85]. While link-cut trees maintain a hierarchy of binary search trees, we maintain a single STT. Most of the complexity of our data structure lies in the implementation of the STT rotation primitive, which can easily be reused, simplifying the development of new STT-based approaches. We implement several variants of our data structure in the Rust programming language, along with an implementation of link-cut trees for comparison. Experimental evaluation suggests that our algorithms are faster when the dynamic forest is unrooted, while link-cut trees are faster for rooted dynamic forests.","url_abs":"https://arxiv.org/abs/2310.18036v2","url_pdf":"https://arxiv.org/pdf/2310.18036v2.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":"fast-and-simple-unrooted-dynamic-forests","repo_url":"https://github.com/berendsohn/stt-rs","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}