{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,23]],"date-time":"2025-10-23T01:34:45Z","timestamp":1761183285749,"version":"build-2065373602"},"reference-count":22,"publisher":"Oxford University Press (OUP)","issue":"10","license":[{"start":{"date-parts":[[2025,5,8]],"date-time":"2025-05-08T00:00:00Z","timestamp":1746662400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000646","name":"JSPS","doi-asserted-by":"publisher","award":["JP20H04140","JP20KK0232","JP21K17706","JP22H03569","JP22K11971","JP23K28037"],"award-info":[{"award-number":["JP20H04140","JP20KK0232","JP21K17706","JP22H03569","JP22K11971","JP23K28037"]}],"id":[{"id":"10.13039\/501100000646","id-type":"DOI","asserted-by":"publisher"}]},{"name":"JST FOREST Program","award":["JPMJFR226U"],"award-info":[{"award-number":["JPMJFR226U"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025,10,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In this paper, we consider the partial gathering problem of mobile agents in dynamic tori. This problem requires $k$ agents distributed in the network to reach a configuration such that either at least $g$ agents or no agent exists at each node. Thus far, in dynamic graphs, partial gathering is considered in 1-interval connected rings, where one of the links in the ring may be missing at each time step. In this paper, we consider another dynamic topology. Concretely, we consider partial gathering in $n\\times n$ dynamic tori such that each of the row and column rings is represented as a 1-interval connected ring. In such networks, when $k = O(gn)$, focusing on the relationship between the values of $k, n$, and $g$, we characterize the solvability of the problem and analyze the move complexity. First, we show that agents cannot solve the problem when $k = o(gn)$. Second, we show that agents can achieve partial gathering with a total number of $O(gn^{3})$ moves when $2gn+2n-1\\le k \\le 2gn + 6n +16g -12$. Finally, we show that agents can achieve partial gathering with a total number of $\\Theta (gn^{2})$ moves when $k\\ge 2gn + 6n +16g -11$.<\/jats:p>","DOI":"10.1093\/comjnl\/bxaf052","type":"journal-article","created":{"date-parts":[[2025,4,25]],"date-time":"2025-04-25T08:12:55Z","timestamp":1745568775000},"page":"1485-1501","source":"Crossref","is-referenced-by-count":0,"title":["Partial gathering of mobile agents in dynamic tori"],"prefix":"10.1093","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1414-8033","authenticated-orcid":false,"given":"Masahiro","family":"Shibata","sequence":"first","affiliation":[{"name":"Graduate School of Computer Science and Systems Engineering , Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka 820-8502,","place":["Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0000-0132-251X","authenticated-orcid":false,"given":"Naoki","family":"Kitamura","sequence":"additional","affiliation":[{"name":"Graduate School of Information Science and Technology , Osaka University, 1-5 Yamadaoka, Suita, Osaka 565-0871,","place":["Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4836-2903","authenticated-orcid":false,"given":"Ryota","family":"Eguchi","sequence":"additional","affiliation":[{"name":"Graduate School of Science and Technology , Nara Institute of Science and Technology, 8916-5 Takayama, Ikoma, Nara 630-0192,","place":["Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4442-1750","authenticated-orcid":false,"given":"Yuichi","family":"Sudo","sequence":"additional","affiliation":[{"name":"Graduate School of Computer and Information Sciences , Hosei University, 3-7-2 Kajino-cho, Koganei-shi, Tokyo 184-8584,","place":["Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1363-4358","authenticated-orcid":false,"given":"Junya","family":"Nakamura","sequence":"additional","affiliation":[{"name":"Information and Media Center , Toyohashi University of Technology, 1-1 Hibarigaoka, Tempaku-cho, Toyohashi, Aichi 441-8580,","place":["Japan"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5437-7626","authenticated-orcid":false,"given":"Yonghwan","family":"Kim","sequence":"additional","affiliation":[{"name":"Graduate School of Computer Science and Engineering , Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, Aichi 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