{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,25]],"date-time":"2025-10-25T12:33:14Z","timestamp":1761395594233},"reference-count":11,"publisher":"World Scientific Pub Co Pte Lt","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2019,9]]},"abstract":"<jats:p> We extend results by Biedl et al. (ISVD\u201913) on the recognition and reconstruction of straight skeletons: Given a geometric tree [Formula: see text], can we recognize whether [Formula: see text] resembles a weighted straight skeleton [Formula: see text] and, if so, can we reconstruct an appropriate polygonal input [Formula: see text] and an appropriate positive weight function [Formula: see text] such that [Formula: see text]? We show that a solution polygon [Formula: see text] and a weight function [Formula: see text] can be found in [Formula: see text] time and space for a geometric tree [Formula: see text] with [Formula: see text] faces if at most one node of [Formula: see text] has two incident edges that span an angle greater than [Formula: see text]. In addition, we show that [Formula: see text] implicitly encodes enough information such that all other weighted bisectors of any solution [Formula: see text] can be obtained from [Formula: see text] without explicitly computing [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0218195919500080","type":"journal-article","created":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T04:16:00Z","timestamp":1571976960000},"page":"251-267","source":"Crossref","is-referenced-by-count":2,"title":["Recognizing Geometric Trees as Positively Weighted Straight Skeletons and Reconstructing Their Input"],"prefix":"10.1142","volume":"29","author":[{"given":"G\u00fcnther","family":"Eder","sequence":"first","affiliation":[{"name":"FB Computerwissenschaften, University of Salzburg, 5020 Salzburg, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martin","family":"Held","sequence":"additional","affiliation":[{"name":"FB Computerwissenschaften, University of Salzburg, 5020 Salzburg, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter","family":"Palfrader","sequence":"additional","affiliation":[{"name":"FB Computerwissenschaften, University of Salzburg, 5020 Salzburg, Austria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2019,10,24]]},"reference":[{"key":"S0218195919500080BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/3-540-61332-3_144"},{"issue":"12","key":"S0218195919500080BIB002","first-page":"752","volume":"1","author":"Aichholzer O.","year":"1995","journal-title":"J. Universal Computer Science"},{"key":"S0218195919500080BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-27261-0_28"},{"key":"S0218195919500080BIB004","doi-asserted-by":"publisher","DOI":"10.1109\/ISVD.2013.11"},{"key":"S0218195919500080BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2014.08.006"},{"key":"S0218195919500080BIB006","doi-asserted-by":"publisher","DOI":"10.1145\/2898961"},{"key":"S0218195919500080BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00453-006-1229-7"},{"key":"S0218195919500080BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/j.ipl.2017.12.001"},{"key":"S0218195919500080BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/PL00009479"},{"key":"S0218195919500080BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.cad.2017.07.003"},{"key":"S0218195919500080BIB011","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195912500124"}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195919500080","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,25]],"date-time":"2019-10-25T04:16:36Z","timestamp":1571976996000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195919500080"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,9]]},"references-count":11,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2019,9]]}},"alternative-id":["10.1142\/S0218195919500080"],"URL":"https:\/\/doi.org\/10.1142\/s0218195919500080","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,9]]}}}