{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:33:31Z","timestamp":1760441611724,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Suppose that a fence needs to be protected (perpetually) by $k$ mobile\u00a0agents with maximum speeds $v_1,\\ldots,v_k$ so that no point on the\u00a0fence is left unattended for more than a given amount of time. The\u00a0problem is to determine if this requirement can be met, and if so, to design a\u00a0suitable patrolling schedule for the agents.\u00a0Alternatively, one would like to find a schedule that minimizes the idle time, that is, the longest time interval during which\u00a0some point is not visited by any agent. We revisit this problem,\u00a0introduced by Czyzowicz et al. (2011), and discuss several strategies\u00a0for the cases where the fence is an open and a closed curve, respectively.In particular:\u00a0(i) we disprove a conjecture by Czyzowicz et al. regarding the\u00a0optimality of their algorithm ${\\mathcal A}_2$ for unidirectional patrolling of a closed fence;\u00a0(ii) we present a schedule with a lower idle time for patrolling\u00a0an open fence, improving an earlier result of Kawamura and Kobayashi.<\/jats:p>","DOI":"10.37236\/4063","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T00:57:23Z","timestamp":1578704243000},"source":"Crossref","is-referenced-by-count":11,"title":["On Fence Patrolling by Mobile Agents"],"prefix":"10.37236","volume":"21","author":[{"given":"Adrian","family":"Dumitrescu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anirban","family":"Ghosh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Csaba D.","family":"T\u00f3th","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2014,7,10]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p4\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i3p4\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T10:55:12Z","timestamp":1579258512000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i3p4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,7,10]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2014,7,3]]}},"URL":"https:\/\/doi.org\/10.37236\/4063","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,7,10]]},"article-number":"P3.4"}}