{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T21:17:59Z","timestamp":1648675079626},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"06","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2013,12]]},"abstract":"<jats:p> In this paper we present a novel nonparametric method for simplifying piecewise linear curves and we apply this method as a statistical approximation of structure within sequential data in the plane. Specifically, given a sequence P of n points in the plane that determine a simple polygonal chain consisting of n\u22121 segments, we describe algorithms for selecting a subsequence Q \u2282 P (including the first and last points of P) that determines a second polygonal chain to approximate P, such that the number of crossings between the two polygonal chains is maximized, and the cardinality of Q is minimized among all such maximizing subsets of P. Our algorithms have respective running times O(n<jats:sup>2<\/jats:sup> log n) (respectively, [Formula: see text]) when P is monotonic and O(n<jats:sup>2<\/jats:sup> log<jats:sup>2<\/jats:sup> n) (respectively, [Formula: see text]) when P is any simple polygonal chain in the Real RAM model (respectively, in the Word RAM model). <\/jats:p>","DOI":"10.1142\/s021819591360011x","type":"journal-article","created":{"date-parts":[[2014,7,15]],"date-time":"2014-07-15T02:29:37Z","timestamp":1405391377000},"page":"427-441","source":"Crossref","is-referenced-by-count":0,"title":["ROBUST NONPARAMETRIC SIMPLIFICATION OF POLYGONAL CHAINS"],"prefix":"10.1142","volume":"23","author":[{"given":"STEPHANE","family":"DUROCHER","sequence":"first","affiliation":[{"name":"University of Manitoba, Winnipeg, Canada"}]},{"given":"ALEXANDRE","family":"LEBLANC","sequence":"additional","affiliation":[{"name":"University of Manitoba, Winnipeg, Canada"}]},{"given":"JASON","family":"MORRISON","sequence":"additional","affiliation":[{"name":"University of Manitoba, Winnipeg, Canada"}]},{"given":"MATTHEW","family":"SKALA","sequence":"additional","affiliation":[{"name":"University of Manitoba, Winnipeg, Canada"}]}],"member":"219","published-online":{"date-parts":[[2014,7,14]]},"reference":[{"key":"p_1","first-page":"195","volume":"2461","author":"Agarwal P. K.","year":"2002","journal-title":"Lecture Notes in Computer Science"},{"key":"p_2","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009500"},{"key":"p_6","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-56279-6_90"},{"key":"p_7","doi-asserted-by":"publisher","DOI":"10.1137\/0217026"},{"key":"p_8","doi-asserted-by":"publisher","DOI":"10.3138\/FM57-6770-U75U-7727"},{"key":"p_9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgor.2003.09.001"},{"key":"p_11","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(98)00027-3"},{"key":"p_15","doi-asserted-by":"publisher","DOI":"10.1016\/j.vibspec.2011.10.016"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021819591360011X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:28:34Z","timestamp":1565188114000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021819591360011X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,12]]},"references-count":8,"journal-issue":{"issue":"06","published-online":{"date-parts":[[2014,7,14]]},"published-print":{"date-parts":[[2013,12]]}},"alternative-id":["10.1142\/S021819591360011X"],"URL":"https:\/\/doi.org\/10.1142\/s021819591360011x","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,12]]}}}