{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T07:16:46Z","timestamp":1683789406686},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2014,12,17]],"date-time":"2014-12-17T00:00:00Z","timestamp":1418774400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2015,1]]},"DOI":"10.1007\/s00454-014-9651-0","type":"journal-article","created":{"date-parts":[[2014,12,16]],"date-time":"2014-12-16T16:01:37Z","timestamp":1418745697000},"page":"80-106","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Most Finite Point Sets in the Plane have Dilation $$>1$$ > 1"],"prefix":"10.1007","volume":"53","author":[{"given":"Rolf","family":"Klein","sequence":"first","affiliation":[]},{"given":"Martin","family":"Kutz","sequence":"additional","affiliation":[]},{"given":"Rainer","family":"Penninger","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,12,17]]},"reference":[{"issue":"1\u20133","key":"9651_CR1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/s00454-007-9019-9","volume":"39","author":"PK Agarwal","year":"2008","unstructured":"Agarwal, P.K., Klein, R., Knauer, C., Langerman, S., Morin, P., Sharir, M., Soss, M.A.: Computing the detour and spanning ratio of paths, trees, and cycles in 2D and 3D. Discrete Comput. Geom. 39(1\u20133), 17\u201337 (2008)","journal-title":"Discrete Comput. Geom."},{"issue":"3","key":"9651_CR2","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/j.comgeo.2007.07.004","volume":"40","author":"B Aronov","year":"2008","unstructured":"Aronov, B., de Berg, M., Cheong, O., Gudmundsson, J., Haverkort, H.J., Smid, M.H.M., Vigneron, A.: Sparse geometric graphs with small dilation. Comput. Geom. 40(3), 207\u2013219 (2008)","journal-title":"Comput. Geom."},{"key":"9651_CR3","unstructured":"Bose, P., Devroye, L., L\u00f6ffler, M., Snoeyink, J., Verma, V.: The spanning ratio of the Delaunay triangulation is greater than $$\\pi \/2$$ \u03c0 \/ 2 . In: CCCG, pp. 165\u2013167 (2009)"},{"key":"9651_CR4","doi-asserted-by":"crossref","unstructured":"Dumitrescu, A., Ebbers-Baumann, A., Gr\u00fcne, A., Klein, R., Rote, G.: On geometric dilation and halving chords. In: Dehne, F.K.H.A., L\u00f3pez-Ortiz, A., Sack, J.-R. (eds.) Algorithms and Data Structures. Proceedings of the 9th International Workshop, WADS 2005, Waterloo, Canada, 15\u201317 August, 2005. Lecture Notes in Computer Science, vol. 3608, pp. 244\u2013255. Springer, Berlin (2005)","DOI":"10.1007\/11534273_22"},{"issue":"1","key":"9651_CR5","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1016\/j.comgeo.2005.07.004","volume":"36","author":"A Dumitrescu","year":"2007","unstructured":"Dumitrescu, A., Ebbers-Baumann, A., Gr\u00fcne, A., Klein, R., Rote, G.: On the geometric dilation of closed curves, graphs, and point sets. Comput. Geom. Theory Appl. 36(1), 16\u201338 (2007)","journal-title":"Comput. Geom. Theory Appl."},{"key":"9651_CR6","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/S0925-7721(03)00046-4","volume":"27","author":"A Ebbers-Baumann","year":"2004","unstructured":"Ebbers-Baumann, A., Klein, R., Langetepe, E., Lingas, A.: A fast algorithm for approximating the detour of a polygonal chain. CGTA Comput. Geom. Theory Appl. 27, 123\u2013134 (2004)","journal-title":"CGTA Comput. Geom. Theory Appl."},{"issue":"2","key":"9651_CR7","doi-asserted-by":"crossref","first-page":"137","DOI":"10.1007\/s00453-005-1203-9","volume":"44","author":"A Ebbers-Baumann","year":"2006","unstructured":"Ebbers-Baumann, A., Gr\u00fcne, A., Klein, R.: The geometric dilation of finite point sets. Algorithmica 44(2), 137\u2013149 (2006)","journal-title":"Algorithmica"},{"issue":"3","key":"9651_CR8","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/j.comgeo.2004.12.009","volume":"37","author":"A Ebbers-Baumann","year":"2007","unstructured":"Ebbers-Baumann, A., Gr\u00fcne, A., Klein, R.: Geometric dilation of closed planar curves: new lower bounds. CGTA Comput. Geom. Theory Appl. 37(3), 188\u2013208 (2007)","journal-title":"CGTA Comput. Geom. Theory Appl."},{"issue":"3","key":"9651_CR9","doi-asserted-by":"crossref","first-page":"201","DOI":"10.1142\/S0218195907002318","volume":"17","author":"A Ebbers-Baumann","year":"2007","unstructured":"Ebbers-Baumann, A., Gr\u00fcne, A., Klein, R., Karpinski, M., Knauer, C., Lingas, A.: Embedding point sets into plane graphs of small dilation. Int. J. Comput. Geom. Appl. (IJCGA) 17(3), 201\u2013230 (2007)","journal-title":"Int. J. Comput. Geom. Appl. (IJCGA)"},{"key":"9651_CR10","volume-title":"Handbook of Computational Geometry","author":"D Eppstein","year":"2000","unstructured":"Eppstein, D.: Spanning trees and spanners. In: Sack, J.R., Urrutia, J. (eds.) Handbook of Computational Geometry. Elsevier, Amsterdam (2000)"},{"key":"9651_CR11","unstructured":"Eppstein, D.: The geometry junkyard. (2014). http:\/\/www.ics.uci.edu\/~eppstein\/junkyard\/dilation-free\/ . Accessed 15 Nov 2014"},{"issue":"1","key":"9651_CR12","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.comgeo.2006.05.007","volume":"37","author":"D Eppstein","year":"2007","unstructured":"Eppstein, D., Wortman, K.A.: Minimum dilation stars. CGTA Comput. Geom. Theory Appl. 37(1), 27\u201337 (2007)","journal-title":"CGTA Comput. Geom. Theory Appl."},{"issue":"1","key":"9651_CR13","doi-asserted-by":"crossref","first-page":"23","DOI":"10.1016\/j.comgeo.2007.07.005","volume":"40","author":"A Gr\u00fcne","year":"2008","unstructured":"Gr\u00fcne, A., Kamali, S.: On the density of iterated line segment intersections. CGTA Comput. Geom. Theory Appl. 40(1), 23\u201336 (2008)","journal-title":"CGTA Comput. Geom. Theory Appl."},{"issue":"3","key":"9651_CR14","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1016\/j.comgeo.2003.10.002","volume":"27","author":"D Ismailescu","year":"2004","unstructured":"Ismailescu, D., Radoi\u010di\u0107, R.: A dense planar point set from iterated line intersections. CGTA Comput. Geom. Theory Appl. 27(3), 257\u2013267 (2004)","journal-title":"CGTA Comput. Geom. Theory Appl."},{"key":"9651_CR15","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1007\/BF02187821","volume":"7","author":"JM Keil","year":"1992","unstructured":"Keil, J.M., Gutwin, C.A.: Classes of graphs which approximate the complete Euclidean graph. Discrete Comput. Geom. 7, 13\u201328 (1992)","journal-title":"Discrete Comput. Geom."},{"key":"9651_CR16","unstructured":"Klein, R., Kutz, M.: The density of iterated crossing points and a gap result for triangulations of finite point sets. In: Amenta, N., Cheong, O. (eds.) Proceedings of the 22nd ACM Symposium on Computational Geometry, Sedona, Arizona, 5\u20137 June, 2006, pp. 264\u2013272. ACM Press, New York (2006)"},{"key":"9651_CR17","unstructured":"Lorenz, D.: On the dilation of finite point sets. Diploma Thesis. Bonn (2005)"},{"key":"9651_CR18","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546884","volume-title":"Geometric Spanner Networks","author":"G Narasimhan","year":"2007","unstructured":"Narasimhan, G., Smid, M.H.M.: Geometric Spanner Networks. Cambridge University Press, Cambridge (2007)"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-014-9651-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-014-9651-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-014-9651-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,18]],"date-time":"2019-08-18T13:55:56Z","timestamp":1566136556000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-014-9651-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,12,17]]},"references-count":18,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2015,1]]}},"alternative-id":["9651"],"URL":"https:\/\/doi.org\/10.1007\/s00454-014-9651-0","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,12,17]]}}}