{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:10:58Z","timestamp":1760440258143},"reference-count":19,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2003,8]]},"abstract":"<jats:p> Given a set of n points S in the Euclidean plane, we address the problem of computing an annulus A, (open region between two concentric circles) of largest width, that partitions S into a subset of points inside and a subset of points outside the circles, such that no point p\u2208S lies in the interior of A. This problem can be considered as a maximin facility location problem for n points such that the facility is a circumference. We give a characterization of the centres of annuli which are locally optimal and we show that the problem can be solved in O(n<jats:sup>3<\/jats:sup> log n) time and O (n) space. We also consider the case in which the number of points in the inner circle is a fixed value k. When k\u2208O(n) our algorithm runs in O(n<jats:sup>3<\/jats:sup> log n) time and O(n) space, furthermore, we can simultaneously optimize for all values of k within the same time bound. When k is small, that is a fixed constant, we can solve the problem in O(n log n) time and O(n) space. <\/jats:p>","DOI":"10.1142\/s0218195903001207","type":"journal-article","created":{"date-parts":[[2004,1,8]],"date-time":"2004-01-08T09:06:00Z","timestamp":1073552760000},"page":"317-325","source":"Crossref","is-referenced-by-count":17,"title":["THE LARGEST EMPTY ANNULUS PROBLEM"],"prefix":"10.1142","volume":"13","author":[{"given":"J. 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A.","family":"SELLAR\u00c8S","sequence":"additional","affiliation":[{"name":"Universitat de Girona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1006\/jagm.1994.1038"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.36.1.84"},{"key":"rf3","volume-title":"Computational Morphology","author":"Bhattacharya B. K.","year":"1988"},{"key":"rf5","first-page":"201","author":"Boffey B.","journal-title":"European J. Oper. Res."},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1016\/0167-8655(90)90080-L"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(96)00070-1"},{"key":"rf9","author":"D\u00edAz-B\u00e1\u00f1ez J. M.","journal-title":"European J. Oper. 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