{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,30]],"date-time":"2022-03-30T15:43:18Z","timestamp":1648654998932},"reference-count":7,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","funder":[{"name":"DOST-SEI ASTHRDP"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2018,3]]},"abstract":"<jats:p> Let [Formula: see text] and [Formula: see text] be two disjoint sets of red points and blue points, respectively, in the plane in general position. Assign a weight [Formula: see text] to each red point and a weight [Formula: see text] to each blue point, where [Formula: see text] and [Formula: see text] are positive integers. Define the weight of a region in the plane as the sum of the weights of red and blue points in it. We give necessary and sufficient conditions for the existence of a line that bisects the weight of the plane whenever the total weight [Formula: see text] is [Formula: see text], for some integer [Formula: see text]. Moreover, we look closely into the special case where [Formula: see text] and [Formula: see text] since this case is important to generate a weight-equitable subdivision of the plane. Among other results, we show that for any configuration of [Formula: see text] with total weight [Formula: see text], for some integer [Formula: see text] and odd integer [Formula: see text], the plane can be subdivided into [Formula: see text] convex regions of weight [Formula: see text] if and only if [Formula: see text]. Using the proofs of the main result, we also give a polynomial time algorithm in finding a weight-equitable subdivision in the plane. <\/jats:p>","DOI":"10.1142\/s0218195918500024","type":"journal-article","created":{"date-parts":[[2018,4,2]],"date-time":"2018-04-02T06:52:29Z","timestamp":1522651949000},"page":"39-56","source":"Crossref","is-referenced-by-count":2,"title":["Weight-Equitable Subdivision of Red and Blue Points in the Plane"],"prefix":"10.1142","volume":"28","author":[{"given":"Jude","family":"Buot","sequence":"first","affiliation":[{"name":"Mathematics Department, Ateneo de Manila University, Quezon City, Philippines"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mikio","family":"Kano","sequence":"additional","affiliation":[{"name":"Ibaraki University, Hitachi, Ibaraki, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2018,4]]},"reference":[{"key":"S0218195918500024BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-55566-4_25"},{"key":"S0218195918500024BIB002","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-42-00925-6"},{"key":"S0218195918500024BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s4540010065"},{"key":"S0218195918500024BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s003730200011"},{"key":"S0218195918500024BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-7721(99)00024-3"},{"key":"S0218195918500024BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-70666-3_9"},{"key":"S0218195918500024BIB008","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195910003426"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195918500024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T13:30:33Z","timestamp":1565184633000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195918500024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3]]},"references-count":7,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2018,4]]},"published-print":{"date-parts":[[2018,3]]}},"alternative-id":["10.1142\/S0218195918500024"],"URL":"https:\/\/doi.org\/10.1142\/s0218195918500024","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3]]}}}