{"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/new-fpt-algorithms-for-finding-the-temporal","title":"New FPT algorithms for finding the temporal hybridization number for sets of phylogenetic trees","arxiv_id":"2007.13615","date":"2020-07-27","proceeding":null,"authors":["Sander Borst","Leo van Iersel","Mark Jones","Steven Kelk"],"abstract":"We study the problem of finding a temporal hybridization network for a set of phylogenetic trees that minimizes the number of reticulations. First, we introduce an FPT algorithm for this problem on an arbitrary set of $m$ binary trees with $n$ leaves each with a running time of $O(5^k\\cdot n\\cdot m)$, where $k$ is the minimum temporal hybridization number. We also present the concept of temporal distance, which is a measure for how close a tree-child network is to being temporal. Then we introduce an algorithm for computing a tree-child network with temporal distance at most $d$ and at most $k$ reticulations in $O((8k)^d5^ k\\cdot n\\cdot m)$ time. Lastly, we introduce a $O(6^kk!\\cdot k\\cdot n^2)$ time algorithm for computing a minimum temporal hybridization network for a set of two nonbinary trees. We also provide an implementation of all algorithms and an experimental analysis on their performance.","url_abs":"http://arxiv.org/abs/2007.13615v1","url_pdf":"http://arxiv.org/pdf/2007.13615v1.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":"new-fpt-algorithms-for-finding-the-temporal","repo_url":"https://github.com/mathcals/temporal_hybridization_number","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}