{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,13]],"date-time":"2024-03-13T11:21:28Z","timestamp":1710328888472},"reference-count":0,"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":[[1993,12]]},"abstract":"<jats:p> In this paper we show that it is impossible to solve a number of \u201cnatural\u201d two-dimensional geometric problems in polylog time with a polynomial number of processors (unless P=NC). Thus, we disprove a popular belief that there are no natural P-complete geometric problems in the plane. The problems we address include instances of polygon triangulation, planar partitioning, and geometric layering. Our results are based on non-trivial reductions from the monotone circuit value and planar circuit value problems. <\/jats:p>","DOI":"10.1142\/s0218195993000282","type":"journal-article","created":{"date-parts":[[2004,11,23]],"date-time":"2004-11-23T03:29:30Z","timestamp":1101180570000},"page":"443-462","source":"Crossref","is-referenced-by-count":9,"title":["P-COMPLETE GEOMETRIC PROBLEMS"],"prefix":"10.1142","volume":"03","author":[{"given":"MIKHAIL J.","family":"ATALLAH","sequence":"first","affiliation":[{"name":"Dept. of Computer Sciences, Purdue Univ., W. Lafayette, IN 47907, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"PAUL B.","family":"CALLAHAN","sequence":"additional","affiliation":[{"name":"Dept. of Computer Science, The Johns Hopkins Univ., Baltimore, MD 21218, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"MICHAEL T.","family":"GOODRICH","sequence":"additional","affiliation":[{"name":"Dept. of Computer Science, The Johns Hopkins Univ., Baltimore, MD 21218, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"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\/S0218195993000282","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T15:36:43Z","timestamp":1565192203000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195993000282"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,12]]},"references-count":0,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[1993,12]]}},"alternative-id":["10.1142\/S0218195993000282"],"URL":"https:\/\/doi.org\/10.1142\/s0218195993000282","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,12]]}}}