{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:12:46Z","timestamp":1760440366337},"reference-count":0,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:p> In this paper, we study the enumerative versions of the interdistance in terdis stance ranking and selection problems in space, namely, the fixed-radius near neighbors and interdistance enumeration problems, respectively. The input to the fixed-radius near neighbors problem is a set of n points S\u2286\u211c<jats:sup>d<\/jats:sup> and a nonnegative real number \u03b4, and the output consists of all pairs of points within interdistance \u03b4. We give an algorithm which, after an O(n log n) time preprocessing step, answers a fixed-radius near neighbors query with respect to an L<jats:sub>p<\/jats:sub> metric in O(n+\u03c1(\u03b4)) time, where \u03c1(\u03b4) is the rank of \u03b4. The space needed is O(n). The input to the interdistance enumeration problem is a set of n points S\u20c4\u211c<jats:sup>d<\/jats:sup> and an integer k, [Formula: see text], and the output is a set of point pairs, each corresponding to an interdistance having length less than or equal to the interdistance with rank k. We offer an O(n log n+k) time, O(n+k) space algorithm for this problem. This algorithm also works for any L<jats:sub>p<\/jats:sub> metric. <\/jats:p>","DOI":"10.1142\/s0218195992000044","type":"journal-article","created":{"date-parts":[[2004,11,25]],"date-time":"2004-11-25T00:50:24Z","timestamp":1101343824000},"page":"49-59","source":"Crossref","is-referenced-by-count":17,"title":["ENUMERATING INTERDISTANCES IN SPACE"],"prefix":"10.1142","volume":"02","author":[{"given":"JEFFREY S.","family":"SALOWE","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Virginia, Thornton Hall, Charlottesville, Virginia 22903, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195992000044","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T23:57:46Z","timestamp":1565135866000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195992000044"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,3]]},"references-count":0,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1992,3]]}},"alternative-id":["10.1142\/S0218195992000044"],"URL":"https:\/\/doi.org\/10.1142\/s0218195992000044","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,3]]}}}