{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:42:29Z","timestamp":1760222549275,"version":"build-2065373602"},"reference-count":9,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2010,7,15]],"date-time":"2010-07-15T00:00:00Z","timestamp":1279152000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Algorithms"],"abstract":"<jats:p>We analyze further the Magnus-Derek game, a two-player game played on a round table with n positions. The players jointly control the movement of a token. One player, Magnus, aims to maximize the number of positions visited while minimizing the number of rounds. The other player, Derek, attempts to minimize the number of visited positions. We present a new strategy for Magnus that succeeds in visiting the maximal number of positions in 3(n \u2013 1) rounds, which is the optimal number of rounds up to a constant factor.<\/jats:p>","DOI":"10.3390\/a3030244","type":"journal-article","created":{"date-parts":[[2010,7,15]],"date-time":"2010-07-15T11:21:21Z","timestamp":1279192881000},"page":"244-254","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["An O(n)-Round Strategy for the Magnus-Derek Game"],"prefix":"10.3390","volume":"3","author":[{"given":"Zhivko","family":"Nedev","sequence":"first","affiliation":[{"name":"International University VNU-HCM, Block 6, Linh Trung Ward, Thu Duc District, HCM City, Vietnam"}]}],"member":"1968","published-online":{"date-parts":[[2010,7,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1016\/j.tcs.2007.11.016","article-title":"The Magnus-Derek Game","volume":"393","author":"Nedev","year":"2008","journal-title":"Theoret. Comput. Sci."},{"key":"ref_2","first-page":"#A45","article-title":"Universal Sets and the Vector Game","volume":"8","author":"Nedev","year":"2008","journal-title":"INTEGERS: Electr. J. Combinat. Number Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"38","DOI":"10.1016\/j.ipl.2008.08.007","article-title":"The Magnus\u2013Derek game revisited","volume":"109","author":"Hurkens","year":"2008","journal-title":"Inf. Proc. Lett."},{"key":"ref_4","unstructured":"Sturmwind, N. Personal communication."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1142\/S179304210800133X","article-title":"Balanced Sets and The Vector Game","volume":"4","author":"Nedev","year":"2008","journal-title":"Int. J. Number Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2259","DOI":"10.1090\/S0025-5718-09-02237-6","article-title":"An algorithm for finding a nearly minimal balanced set in \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t          \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t            \n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t         F\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t p","volume":"78","author":"Nedev","year":"2009","journal-title":"Math. Comput."},{"key":"ref_7","unstructured":"Sloane, N. On line Encyclopedia of Sequences. Availible online: http:\/\/www.research.att.com\/ njas\/sequences\/."},{"key":"ref_8","first-page":"99","article-title":"Recherches sur les nombres","volume":"9","author":"Cauchy","year":"1813","journal-title":"J. Ec. Polytech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1112\/jlms\/s1-10.37.30","article-title":"On the addition of residue classes","volume":"10","author":"Davenport","year":"1935","journal-title":"J. Lond. Math. Soc."}],"container-title":["Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1999-4893\/3\/3\/244\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T22:02:56Z","timestamp":1760220176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1999-4893\/3\/3\/244"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,15]]},"references-count":9,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2010,9]]}},"alternative-id":["a3030244"],"URL":"https:\/\/doi.org\/10.3390\/a3030244","relation":{},"ISSN":["1999-4893"],"issn-type":[{"type":"electronic","value":"1999-4893"}],"subject":[],"published":{"date-parts":[[2010,7,15]]}}}