{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,8]],"date-time":"2026-01-08T01:06:57Z","timestamp":1767834417008,"version":"3.49.0"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2009,12,29]],"date-time":"2009-12-29T00:00:00Z","timestamp":1262044800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2010,3]]},"DOI":"10.1007\/s00454-009-9235-6","type":"journal-article","created":{"date-parts":[[2009,12,28]],"date-time":"2009-12-28T14:55:54Z","timestamp":1262012154000},"page":"375-392","source":"Crossref","is-referenced-by-count":38,"title":["Greedy Drawings of Triangulations"],"prefix":"10.1007","volume":"43","author":[{"given":"Raghavan","family":"Dhandapani","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2009,12,29]]},"reference":[{"key":"9235_CR1","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1007\/s00453-006-0177-6","volume":"47","author":"N. Bonichon","year":"2007","unstructured":"Bonichon, N., Felsner, S., Mosbah, M.: Convex drawings of 3-connected planar graphs. Algorithmica 47, 399\u2013420 (2007)","journal-title":"Algorithmica"},{"key":"9235_CR2","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1145\/313239.313282","volume-title":"DIALM \u201999: Proceedings of the 3rd International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications","author":"P. Bose","year":"1999","unstructured":"Bose, P., Morin, P., Stojmenovic, I., Urrutia, J.: Routing with guaranteed delivery in ad hoc wireless networks. In: DIALM \u201999: Proceedings of the 3rd International Workshop on Discrete Algorithms and Methods for Mobile Computing and Communications, pp. 48\u201355. ACM, New York (1999)"},{"key":"9235_CR3","unstructured":"Brehm, E.: 3-orientations and Schnyder 3-tree decompositions. Diplomarbeit, Freie Universitat, Berlin (2000)"},{"key":"9235_CR4","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1145\/62212.62254","volume-title":"STOC \u201988: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing","author":"H. Fraysseix de","year":"1988","unstructured":"de Fraysseix, H., Pach, J., Pollack, R.: Small sets supporting f\u00e1ry embeddings of planar graphs. In: STOC \u201988: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, pp.\u00a0426\u2013433. ACM, New York (1988)"},{"key":"9235_CR5","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1023\/A:1010604726900","volume":"18","author":"S. Felsner","year":"2001","unstructured":"Felsner, S.: Convex drawings of planar graphs and the order dimension of 3-polytopes. Order 18, 19\u201337 (2001)","journal-title":"Order"},{"key":"9235_CR6","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-322-80303-0","volume-title":"Geometric Graphs and Arrangements","author":"S. Felsner","year":"2004","unstructured":"Felsner, S.: Geometric Graphs and Arrangements. Vieweg, Wiesbaden (2004)"},{"key":"9235_CR7","first-page":"690","volume-title":"SODA \u201905: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms","author":"E. Fusy","year":"2005","unstructured":"Fusy, E., Poulalhon, D., Schaeffer, G.: Dissections and trees, with applications to optimal mesh encoding and to random sampling. In: SODA \u201905: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.\u00a0690\u2013699. Society for Industrial and Applied Mathematics, Philadelphia (2005)"},{"key":"9235_CR8","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1145\/501416.501424","volume-title":"MobiHoc \u201901: Proceedings of the 2nd ACM International Symposium on Mobile Ad Hoc Networking & Computing","author":"J. Gao","year":"2001","unstructured":"Gao, J., Guibas, L.J., Hershberger, J., Zhang, L., Zhu, A.: Geometric spanner for routing in mobile networks. In: MobiHoc \u201901: Proceedings of the 2nd ACM International Symposium on Mobile Ad Hoc Networking & Computing, pp.\u00a045\u201355. ACM, New York (2001)"},{"issue":"4","key":"9235_CR9","doi-asserted-by":"crossref","first-page":"549","DOI":"10.1145\/321850.321852","volume":"21","author":"J. Hopcroft","year":"1974","unstructured":"Hopcroft, J., Tarjan, R.: Efficient planarity testing. J. ACM 21(4), 549\u2013568 (1974)","journal-title":"J. ACM"},{"key":"9235_CR10","doi-asserted-by":"crossref","unstructured":"Kant, G.: Drawing planar graphs using the lmc-ordering. In: Foundations of Computer Science, Proceedings, 33rd Annual Symposium on, pp. 101\u2013110 (1992)","DOI":"10.1109\/SFCS.1992.267814"},{"key":"9235_CR11","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1145\/345910.345953","volume-title":"MobiCom \u201900: Proceedings of the 6th Annual International Conference on Mobile Computing and Networking","author":"B. Karp","year":"2000","unstructured":"Karp, B., Kung, H.T.: GPSR: Greedy perimeter stateless routing for wireless networks. In: MobiCom \u201900: Proceedings of the 6th Annual International Conference on Mobile Computing and Networking, pp.\u00a0243\u2013254. ACM, New York (2000)"},{"key":"9235_CR12","doi-asserted-by":"crossref","first-page":"132","DOI":"10.4064\/fm-14-1-132-137","volume":"14","author":"B. Knaster","year":"1929","unstructured":"Knaster, B., Kuratowski, C., Mazurkiewicz, C.: Ein Beweis des Fixpunktsatzes fur n-dimensionale Simplexe. Fundam. Math. 14, 132\u2013137 (1929)","journal-title":"Fundam. Math."},{"key":"9235_CR13","unstructured":"Kleinberg, R.: Personal communication (2006)"},{"key":"9235_CR14","unstructured":"Kleinberg, R.: Geographic routing in hyperbolic space. In: Workshop on Parallelism in Algorithms and Architectures. University of Maryland, College Park, May 12, 2006"},{"key":"9235_CR15","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1145\/872035.872044","volume-title":"PODC \u201903: Proceedings of the Twenty-Second Annual Symposium on Principles of Distributed Computing","author":"F. Kuhn","year":"2003","unstructured":"Kuhn, F., Wattenhofer, R., Zhang, Y., Zollinger, A.: Geometric ad-hoc routing: of theory and practice. In: PODC \u201903: Proceedings of the Twenty-Second Annual Symposium on Principles of Distributed Computing, pp.\u00a063\u201372. ACM, New York (2003)"},{"issue":"1","key":"9235_CR16","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1007\/BF02122557","volume":"8","author":"N. Linial","year":"1988","unstructured":"Linial, N., Lovasz, L., Wigderson, A.: Rubber bands, convex embeddings and graph connectivity. Combinatorica 8(1), 91\u2013102 (1988)","journal-title":"Combinatorica"},{"key":"9235_CR17","volume-title":"Using the Borsuk\u2013Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry","author":"J. Matou\u0161ek","year":"2007","unstructured":"Matou\u0161ek, J.: Using the Borsuk\u2013Ulam Theorem: Lectures on Topological Methods in Combinatorics and Geometry. Springer, Berlin (2007)"},{"key":"9235_CR18","unstructured":"Maymounkov, P.: Greedy embeddings, trees, and Euclidean vs. Lobachevsky geometry (manuscript, 2006)"},{"key":"9235_CR19","doi-asserted-by":"crossref","DOI":"10.1142\/5648","volume-title":"Planar Graph Drawing","author":"T. Nishizeki","year":"2004","unstructured":"Nishizeki, T., Rahman, S.: Planar Graph Drawing. World Scientific, Singapore (2004)"},{"issue":"1","key":"9235_CR20","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/j.tcs.2005.06.022","volume":"344","author":"C.H. Papadimitriou","year":"2005","unstructured":"Papadimitriou, C.H., Ratajczak, D.: On a conjecture related to geometric routing. Theor. Comput. Sci. 344(1), 3\u201314 (2005)","journal-title":"Theor. Comput. Sci."},{"key":"9235_CR21","first-page":"728","volume-title":"SODA \u201905: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms","author":"G. Rote","year":"2005","unstructured":"Rote, G.: Strictly convex drawings of planar graphs. In: SODA \u201905: Proceedings of the Sixteenth Annual ACM-SIAM Symposium on Discrete Algorithms, pp.\u00a0728\u2013734. Society for Industrial and Applied Mathematics, Philadelphia (2005)"},{"key":"9235_CR22","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1145\/938985.938996","volume-title":"MobiCom \u201903: Proceedings of the 9th Annual International Conference on Mobile Computing and Networking","author":"A. Rao","year":"2003","unstructured":"Rao, A., Papadimitriou, C., Shenker, S., Stoica, I.: Geographic routing without location information. In: MobiCom \u201903: Proceedings of the 9th Annual International Conference on Mobile Computing and Networking, pp.\u00a096\u2013108. ACM, New York (2003)"},{"key":"9235_CR23","first-page":"138","volume-title":"SODA \u201990: Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms","author":"W. Schnyder","year":"1990","unstructured":"Schnyder, W.: Embedding planar graphs on the grid. In: SODA \u201990: Proceedings of the First Annual ACM-SIAM Symposium on Discrete Algorithms, pp.\u00a0138\u2013148. Society for Industrial and Applied Mathematics, Philadelphia (1990)"},{"key":"9235_CR24","volume-title":"Graph Drawing: Algorithms for the Visualization of Graphs","author":"I.G. Tollis","year":"1998","unstructured":"Tollis, I.G., Di Battista, G., Eades, P., Tamassia, R.: Graph Drawing: Algorithms for the Visualization of Graphs. Prentice Hall, New York (1998)"},{"key":"9235_CR25","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1090\/S0002-9947-1956-0081471-8","volume":"82","author":"W.T. Tutte","year":"1956","unstructured":"Tutte, W.T.: A theorem on planar graphs. Trans. Am. Math. Soc. 82, 99\u2013116 (1956)","journal-title":"Trans. Am. Math. Soc."},{"key":"9235_CR26","doi-asserted-by":"crossref","unstructured":"Tutte, W.T.: Convex representations of graphs. In: Proceedings of the London Mathematical Society, pp. 304\u2013320 (1960)","DOI":"10.1112\/plms\/s3-10.1.304"}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-009-9235-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-009-9235-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-009-9235-6","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T23:50:31Z","timestamp":1559087431000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-009-9235-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,12,29]]},"references-count":26,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2010,3]]}},"alternative-id":["9235"],"URL":"https:\/\/doi.org\/10.1007\/s00454-009-9235-6","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,12,29]]}}}