{"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/a-discrete-and-bounded-envy-free-cake-cutting","title":"A Discrete and Bounded Envy-Free Cake Cutting Protocol for Any Number of Agents","arxiv_id":"1604.03655","date":"2016-04-13","proceeding":null,"authors":["Haris Aziz","Simon Mackenzie"],"abstract":"We consider the well-studied cake cutting problem in which the goal is to\nfind an envy-free allocation based on queries from $n$ agents. The problem has\nreceived attention in computer science, mathematics, and economics. It has been\na major open problem whether there exists a discrete and bounded envy-free\nprotocol. We resolve the problem by proposing a discrete and bounded envy-free\nprotocol for any number of agents. The maximum number of queries required by\nthe protocol is $n^{n^{n^{n^{n^n}}}}$. We additionally show that even if we do\nnot run our protocol to completion, it can find in at most $n^3{(n^2)}^n$\nqueries a partial allocation of the cake that achieves proportionality (each\nagent gets at least $1/n$ of the value of the whole cake) and envy-freeness.\nFinally we show that an envy-free partial allocation can be computed in at most\n$n^3{(n^2)}^n$ queries such that each agent gets a connected piece that gives\nthe agent at least $1/(3n)$ of the value of the whole cake.","url_abs":"http://arxiv.org/abs/1604.03655v12","url_pdf":"http://arxiv.org/pdf/1604.03655v12.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":"abstracts"},"code_links":[{"paper_slug":"a-discrete-and-bounded-envy-free-cake-cutting","repo_url":"https://github.com/cowtrix/kake","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}