{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,21]],"date-time":"2026-07-21T22:35:18Z","timestamp":1784673318764,"version":"3.55.0"},"reference-count":14,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Found. Comput. Sci."],"published-print":{"date-parts":[[2009,2]]},"abstract":"<jats:p> Given a connected geometric graph G, we consider the problem of constructing a t-spanner of G having the minimum number of edges. We prove that for every real number t with [Formula: see text], there exists a connected geometric graph G with n vertices, such that every t-spanner of G contains \u03a9(n<jats:sup>1+1\/t<\/jats:sup>) edges. This bound almost matches the known upper bound, which states that every connected weighted graph with n vertices contains a t-spanner with O(n<jats:sup>1+2\/(t-1)<\/jats:sup>) edges. We also prove that the problem of deciding whether a given geometric graph contains a t-spanner with at most K edges is NP-hard. Previously, this NP-hardness result was only known for non-geometric graphs. <\/jats:p>","DOI":"10.1142\/s0129054109006486","type":"journal-article","created":{"date-parts":[[2009,2,17]],"date-time":"2009-02-17T10:16:23Z","timestamp":1234865783000},"page":"135-149","source":"Crossref","is-referenced-by-count":6,"title":["ON SPANNERS OF GEOMETRIC GRAPHS"],"prefix":"10.1142","volume":"20","author":[{"given":"JOACHIM","family":"GUDMUNDSSON","sequence":"first","affiliation":[{"name":"National ICT Australia Ltd., Sydney, Australia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"MICHIEL","family":"SMID","sequence":"additional","affiliation":[{"name":"School of Computer Science, Carleton University, Ottawa, Ontario, Canada K1S 5B6, Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02189308"},{"key":"rf2","first-page":"1","volume":"3","author":"Brandes U.","journal-title":"Discrete Mathematics and Theoretical Computer Science"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/0166-218X(94)90073-6"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480192237403"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1137\/S0895480101387893"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044482537-7\/50010-3"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1201\/9781420010749.ch52"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546884"},{"key":"rf14","series-title":"Society for Industrial and Applied Mathematics","volume-title":"Monographs on Discrete Mathematics and Applications","author":"Peleg D.","year":"2000"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190130114"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195991000098"},{"key":"rf17","doi-asserted-by":"publisher","DOI":"10.1016\/B978-044482537-7\/50021-8"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.1007\/BF02574695"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1006\/inco.1997.2641"}],"container-title":["International Journal of Foundations of Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0129054109006486","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:39:30Z","timestamp":1565095170000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0129054109006486"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,2]]},"references-count":14,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2012,4,30]]},"published-print":{"date-parts":[[2009,2]]}},"alternative-id":["10.1142\/S0129054109006486"],"URL":"https:\/\/doi.org\/10.1142\/s0129054109006486","relation":{},"ISSN":["0129-0541","1793-6373"],"issn-type":[{"value":"0129-0541","type":"print"},{"value":"1793-6373","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,2]]}}}