{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T22:25:20Z","timestamp":1648938320412},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"04","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2011,12]]},"abstract":"<jats:p> The Steiner minimum tree and the minimum spanning tree are two important problems in combinatorial optimization. Let P denote a finite set of points, called terminals, in the Euclidean space. A Steiner minimum tree of P, denoted by SMT(P), is a network with minimum length to interconnect all terminals, and a minimum spanning tree of P, denoted by MST(P), is also a minimum network interconnecting all the points in P, however, subject to the constraint that all the line segments in it have to terminate at terminals. Therefore, SMT(P) may contain points not in P, but MST(P) cannot contain such kind of points. Let [Formula: see text] denote the n-dimensional Euclidean space. The Steiner ratio in [Formula: see text] is defined to be [Formula: see text], where L<jats:sub>s<\/jats:sub>(P) and L<jats:sub>m<\/jats:sub>(P), respectively, denote lengths of a Steiner minimum tree and a minimum spanning tree of P. The best previously known lower bound for [Formula: see text] in the literature is 0.615. In this paper, we show that [Formula: see text] for any n \u2265 2. <\/jats:p>","DOI":"10.1142\/s1793830911001358","type":"journal-article","created":{"date-parts":[[2012,1,4]],"date-time":"2012-01-04T14:00:28Z","timestamp":1325685628000},"page":"473-489","source":"Crossref","is-referenced-by-count":0,"title":["ON THE STEINER RATIO IN $\\mathcal{R}_{n}$"],"prefix":"10.1142","volume":"03","author":[{"given":"HAI","family":"DU","sequence":"first","affiliation":[{"name":"School of Science, Xi'an Jiaotong University, Xi'an, 710049, P. R. China"},{"name":"School of Management, Xi'an Jiaotong University, Xi'an, 710049, P. R. China"},{"name":"Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi'an, 710049, P. R. China"}]},{"given":"WEILI","family":"WU","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, TX 75081, USA"}]},{"given":"ZAIXIN","family":"LU","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at Dallas, Richardson, TX 75081, USA"}]},{"given":"YINFENG","family":"XU","sequence":"additional","affiliation":[{"name":"School of Science, Xi'an Jiaotong University, Xi'an, 710049, P. R. China"},{"name":"School of Management, Xi'an Jiaotong University, Xi'an, 710049, P. R. China"},{"name":"Ministry of Education Key Lab for Intelligent Networks and Network Security, Xi'an, 710049, P. R. China"}]}],"member":"219","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"rf1","first-page":"313","volume":"4","author":"Chung F. R. K.","journal-title":"Bull. Inst. Math. Acad. Sin."},{"key":"rf2","unstructured":"V. F.\u00a0Dernyanov and V. N.\u00a0Malozernov, Introduction to Minimax (Dover Publication Inc., New York, 1990)\u00a0pp. 218\u2013221."},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF02071981"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1006\/jcta.1996.0040"},{"key":"rf5","doi-asserted-by":"publisher","DOI":"10.1137\/0116001"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830911001358","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T21:40:41Z","timestamp":1565127641000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830911001358"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,12]]},"references-count":5,"journal-issue":{"issue":"04","published-online":{"date-parts":[[2012,4,5]]},"published-print":{"date-parts":[[2011,12]]}},"alternative-id":["10.1142\/S1793830911001358"],"URL":"https:\/\/doi.org\/10.1142\/s1793830911001358","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,12]]}}}