{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,28]],"date-time":"2025-10-28T03:08:33Z","timestamp":1761620913200},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"05","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Comput. Geom. Appl."],"published-print":{"date-parts":[[2005,10]]},"abstract":"<jats:p> In the following we show that any convex set that contains a congruent copy of any set of diameter one (universal cover) has area at least 0.832. This considerably improves the lower bound for Lebesgue's universal cover problem, using a combination of computer search and geometric bounds. <\/jats:p>","DOI":"10.1142\/s0218195905001828","type":"journal-article","created":{"date-parts":[[2005,10,19]],"date-time":"2005-10-19T10:07:45Z","timestamp":1129716465000},"page":"537-544","source":"Crossref","is-referenced-by-count":8,"title":["A LOWER BOUND FOR LEBESGUE'S UNIVERSAL COVER PROBLEM"],"prefix":"10.1142","volume":"15","author":[{"given":"PETER","family":"BRASS","sequence":"first","affiliation":[{"name":"Department of Computer Science,  City College of New York, 138th Street at Convent Avenue,  New York, NY 10031, USA"}]},{"given":"MEHRBOD","family":"SHARIFI","sequence":"additional","affiliation":[]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","first-page":"35","volume":"3","author":"P\u00e1l J.","journal-title":"Math.-fys. Medd., Danske Vid. Selsk."},{"key":"rf2","volume-title":"Research Problems in Discrete Geometry","author":"Brass P.","year":"2005"},{"key":"rf3","first-page":"34","volume":"15","author":"Wetzel J. E.","journal-title":"Geombinatorics"},{"key":"rf4","first-page":"241","volume":"123","author":"Jung H. W. E.","journal-title":"J. Reine Angew. Math."},{"key":"rf5","first-page":"310","volume":"137","author":"Jung H. W. E.","journal-title":"J. Reine Angew. Math."},{"key":"rf6","first-page":"96","author":"Sprague R.","journal-title":"Mat. Tidsskr. Ser. B"},{"key":"rf7","first-page":"37","volume":"2","author":"Duff G. F. D.","journal-title":"C. R. Math. Rep. Acad. Sci. Canada"},{"key":"rf8","first-page":"165","volume":"4","author":"Hansen H. C.","journal-title":"Geometriae Dedicata"},{"key":"rf9","first-page":"115","volume":"29","author":"Hansen H. C.","journal-title":"Normat"},{"key":"rf10","first-page":"205","volume":"42","author":"Hansen H. C.","journal-title":"Geometriae Dedicata"},{"key":"rf11","doi-asserted-by":"publisher","DOI":"10.1007\/BF02759701"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-322-98556-9"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574391"},{"key":"rf14","first-page":"473","volume":"39","author":"Bezdek K.","journal-title":"Beitr\u00e4ge Algebra Geom."}],"container-title":["International Journal of Computational Geometry &amp; Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218195905001828","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T00:29:16Z","timestamp":1565137756000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218195905001828"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,10]]},"references-count":14,"journal-issue":{"issue":"05","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2005,10]]}},"alternative-id":["10.1142\/S0218195905001828"],"URL":"https:\/\/doi.org\/10.1142\/s0218195905001828","relation":{},"ISSN":["0218-1959","1793-6357"],"issn-type":[{"value":"0218-1959","type":"print"},{"value":"1793-6357","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,10]]}}}