{"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/improved-lower-bounds-for-queen-s-domination","title":"Improved lower bounds for Queen's Domination via an exactly-solvable relaxation","arxiv_id":"2304.06620","date":"2023-04-13","proceeding":null,"authors":["Archit Karandikar","Akashnil Dutta"],"abstract":"The Queen's Domination problem, studied for over 160 years, poses the following question: What is the least number of queens that can be arranged on a $m \\times n$ chessboard so that they either attack or occupy every cell? We propose a novel relaxation of the Queen's Domination problem and show that it is exactly solvable on both square and rectangular chessboards. As a consequence, we improve on the best known lower bound for rectangular chessboards in $\\approx 12.5\\%$ of the non-trivial cases. As another consequence, we simplify and generalize the proofs for the best known lower-bounds for Queen's Domination of square $n \\times n$ chessboards for $n \\equiv \\{0,1,2\\} \\mod 4$ using an elegant idea based on a convex hull. Finally, we show some results and make some conjectures towards the goal of simplifying the long complicated proof for the best known lower-bound for square boards when $n \\equiv 3 \\mod 4$ (and $n > 11$). These simple-to-state conjectures may also be of independent interest.","url_abs":"https://arxiv.org/abs/2304.06620v1","url_pdf":"https://arxiv.org/pdf/2304.06620v1.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":"improved-lower-bounds-for-queen-s-domination","repo_url":"https://github.com/architkarandikar/queens-domination","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"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}