{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,5]],"date-time":"2025-10-05T04:36:05Z","timestamp":1759638965182},"reference-count":9,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2010,6]]},"abstract":"<jats:p> We discuss two versions of the Fr\u00e9chet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance between two points is the length of the shortest path between the points. In both cases, we give algorithms for finding a (1 + \u220a)-factor approximation of the Fr\u00e9chet distance between two polygonal curves. We also consider the Fr\u00e9chet distance between two polygonal curves among polyhedral obstacles in [Formula: see text] (1\/\u221e weighted region problem) and present a (1 + \u220a)-factor approximation algorithm. <\/jats:p>","DOI":"10.1142\/s1793830910000644","type":"journal-article","created":{"date-parts":[[2010,7,5]],"date-time":"2010-07-05T06:31:23Z","timestamp":1278311483000},"page":"161-179","source":"Crossref","is-referenced-by-count":1,"title":["FR\u00c9CHET DISTANCE PROBLEMS IN WEIGHTED REGIONS"],"prefix":"10.1142","volume":"02","author":[{"given":"YAM KI","family":"CHEUNG","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA"}]},{"given":"OVIDIU","family":"DAESCU","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, TX 75080, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","series-title":"Lect. Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/11821069_9","volume":"4162","author":"Aleksandrov L.","year":"2006"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1145\/1044731.1044733"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195995000064"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1023\/A:1009885517653"},{"key":"rf13","series-title":"Lect. Notes in Comput. Sci.","doi-asserted-by":"crossref","first-page":"134","DOI":"10.1007\/3-540-07407-4_17","volume":"33","author":"Collins G. E.","year":"1975"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1007\/BF03018603"},{"key":"rf17","volume-title":"Spectrochemical Analysis","author":"Ingle J. D. J.","year":"1988"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1145\/102782.102784"},{"key":"rf21","doi-asserted-by":"publisher","DOI":"10.1016\/j.jalgor.2004.07.004"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830910000644","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:20:36Z","timestamp":1565126436000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830910000644"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,6]]},"references-count":9,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2010,6]]}},"alternative-id":["10.1142\/S1793830910000644"],"URL":"https:\/\/doi.org\/10.1142\/s1793830910000644","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,6]]}}}