{"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/cones-of-weighted-and-partial-metrics","title":"Cones of Weighted and Partial Metrics","arxiv_id":"1101.0517","date":"2011-01-03","proceeding":null,"authors":["Michel Deza","Elena Deza","Janoš Vidali"],"abstract":"A partial semimetric on V_n={1, ..., n} is a function f=((f_{ij})): V_n^2 -> R_>=0 satisfying f_ij=f_ji >= f_ii and f_ij+f_ik-f_jk-f_ii >= 0 for all i,j,k in V_n. The function f is a weak partial semimetric if f_ij >= f_ii is dropped, and it is a strong partial semimetric if f_ij >= f_ii is complemented by f_ij <= f_ii+f_jj. We describe the cones of weak and strong partial semimetrics via corresponding weighted semimetrics and list their 0,1-valued elements, identifying when they belong to extreme rays. We consider also related cones, including those of partial hypermetrics, weighted hypermetrics, l_1-quasi semimetrics and weighted/partial cuts.","url_abs":"http://arxiv.org/abs/1101.0517v3","url_pdf":"http://arxiv.org/pdf/1101.0517v3.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":"cones-of-weighted-and-partial-metrics","repo_url":"https://github.com/jaanos/jaanos.github.io","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"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}