{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T03:56:30Z","timestamp":1767239790407,"version":"3.41.0"},"publisher-location":"Cham","reference-count":21,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783319501055"},{"type":"electronic","value":"9783319501062"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-319-50106-2_40","type":"book-chapter","created":{"date-parts":[[2016,12,7]],"date-time":"2016-12-07T15:22:42Z","timestamp":1481124162000},"page":"519-531","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Gabriel Triangulations and Angle-Monotone Graphs: Local Routing and Recognition"],"prefix":"10.1007","author":[{"given":"Nicolas","family":"Bonichon","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Prosenjit","family":"Bose","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paz","family":"Carmi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Irina","family":"Kostitsyna","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anna","family":"Lubiw","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sander","family":"Verdonschot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,12,8]]},"reference":[{"issue":"1\u20132","key":"40_CR1","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/S0166-218X(00)00233-X","volume":"109","author":"O Aichholzer","year":"2001","unstructured":"Aichholzer, O., Aurenhammer, F., Icking, C., Klein, R., Langetepe, E., Rote, G.: Generalized self-approaching curves. Discrete Appl. Math. 109(1\u20132), 3\u201324 (2001)","journal-title":"Discrete Appl. Math."},{"key":"40_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"260","DOI":"10.1007\/978-3-642-36763-2_23","volume-title":"Graph Drawing","author":"S Alamdari","year":"2013","unstructured":"Alamdari, S., Chan, T.M., Grant, E., Lubiw, A., Pathak, V.: Self-approaching Graphs. In: Didimo, W., Patrignani, M. (eds.) GD 2012. LNCS, vol. 7704, pp. 260\u2013271. Springer, Heidelberg (2013). doi: 10.1007\/978-3-642-36763-2_23"},{"doi-asserted-by":"crossref","unstructured":"Angelini, P.: Monotone drawings of graphs with few directions. In: 6th International Conference on Information, Intelligence, Systems and Applications (IISA), pp. 1\u20136. IEEE (2015)","key":"40_CR3","DOI":"10.1109\/IISA.2015.7388003"},{"issue":"1","key":"40_CR4","doi-asserted-by":"publisher","first-page":"5","DOI":"10.7155\/jgaa.00249","volume":"16","author":"P Angelini","year":"2012","unstructured":"Angelini, P., Colasante, E., Battista, G.D., Frati, F., Patrignani, M.: Monotone drawings of graphs. J. Graph Algorithms Appl. 16(1), 5\u201335 (2012)","journal-title":"J. Graph Algorithms Appl."},{"issue":"1","key":"40_CR5","doi-asserted-by":"publisher","first-page":"19","DOI":"10.7155\/jgaa.00197","volume":"14","author":"P Angelini","year":"2010","unstructured":"Angelini, P., Frati, F., Grilli, L.: An algorithm to construct greedy drawings of triangulations. J. Graph Algorithms Appl. 14(1), 19\u201351 (2010)","journal-title":"J. Graph Algorithms Appl."},{"doi-asserted-by":"crossref","unstructured":"Bern, M., Eppstein, D., Gilbert, J.: Provably good mesh generation. In: Proceedings of 31st Symposium on Foundations of Computer Science (FOCS), pp. 231\u2013241. IEEE (1990)","key":"40_CR6","DOI":"10.1109\/FSCS.1990.89542"},{"key":"40_CR7","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/978-3-662-48350-3_18","volume-title":"Algorithms \u2013 ESA 2015","author":"N Bonichon","year":"2015","unstructured":"Bonichon, N., Bose, P., Carufel, J.-L., Perkovi\u0107, L., Renssen, A.: Upper and lower bounds for online routing on Delaunay triangulations. In: Bansal, N., Finocchi, I. (eds.) ESA 2015. LNCS, vol. 9294, pp. 203\u2013214. Springer, Heidelberg (2015). doi: 10.1007\/978-3-662-48350-3_18"},{"key":"40_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"266","DOI":"10.1007\/978-3-642-16926-7_25","volume-title":"Graph Theoretic Concepts in Computer Science","author":"N Bonichon","year":"2010","unstructured":"Bonichon, N., Gavoille, C., Hanusse, N., Ilcinkas, D.: Connections between theta-graphs, delaunay triangulations, and orthogonal surfaces. In: Thilikos, D.M. (ed.) WG 2010. LNCS, vol. 6410, pp. 266\u2013278. Springer, Heidelberg (2010). doi: 10.1007\/978-3-642-16926-7_25"},{"issue":"6","key":"40_CR9","doi-asserted-by":"publisher","first-page":"1626","DOI":"10.1137\/140988103","volume":"44","author":"P Bose","year":"2015","unstructured":"Bose, P., Fagerberg, R., van Renssen, A., Verdonschot, S.: Optimal local routing on Delaunay triangulations defined by empty equilateral triangles. SIAM J. Comput. 44(6), 1626\u20131649 (2015)","journal-title":"SIAM J. Comput."},{"doi-asserted-by":"crossref","unstructured":"Chew, L.P.: There is a planar graph almost as good as the complete graph. In: Proceedings of 2nd Annual Symposium Computational Geometry (SoCG), pp. 169\u2013177 (1986)","key":"40_CR10","DOI":"10.1145\/10515.10534"},{"issue":"2","key":"40_CR11","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/0022-0000(89)90044-5","volume":"39","author":"LP Chew","year":"1989","unstructured":"Chew, L.P.: There are planar graphs almost as good as the complete graph. J. Comput. Syst. Sci. 39(2), 205\u2013219 (1989)","journal-title":"J. Comput. Syst. Sci."},{"issue":"2","key":"40_CR12","doi-asserted-by":"publisher","first-page":"761","DOI":"10.7155\/jgaa.00348","volume":"19","author":"HR Dehkordi","year":"2015","unstructured":"Dehkordi, H.R., Frati, F., Gudmundsson, J.: Increasing-chord graphs on point sets. J. Graph Algorithms Appl. 19(2), 761\u2013778 (2015)","journal-title":"J. Graph Algorithms Appl."},{"key":"40_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/978-3-319-29221-2_12","volume-title":"Algorithms and Discrete Applied Mathematics","author":"A Dumitrescu","year":"2016","unstructured":"Dumitrescu, A., Ghosh, A.: Lower bounds on the dilation of plane spanners. In: Govindarajan, S., Maheshwari, A. (eds.) CALDAM 2016. LNCS, vol. 9602, pp. 139\u2013151. Springer, Heidelberg (2016). doi: 10.1007\/978-3-319-29221-2_12 . http:\/\/arxiv.org\/pdf\/1509.07181v3.pdf"},{"key":"40_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"729","DOI":"10.1007\/978-3-662-48350-3_61","volume-title":"Algorithms \u2013 ESA 2015","author":"X He","year":"2015","unstructured":"He, X., He, D.: Monotone drawings of 3-connected plane graphs. In: Bansal, N., Finocchi, I. (eds.) ESA 2015. LNCS, vol. 9294, pp. 729\u2013741. Springer, Heidelberg (2015). doi: 10.1007\/978-3-662-48350-3_61"},{"key":"40_CR15","doi-asserted-by":"publisher","first-page":"441","DOI":"10.1017\/S0305004198003016","volume":"125","author":"C Icking","year":"1995","unstructured":"Icking, C., Klein, R., Langetepe, E.: Self-approaching curves. Math. Proc. Camb. Philos. Soc. 125, 441\u2013453 (1995)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"40_CR16","doi-asserted-by":"publisher","first-page":"686","DOI":"10.1007\/s00454-009-9227-6","volume":"44","author":"T Leighton","year":"2010","unstructured":"Leighton, T., Moitra, A.: Some results on greedy embeddings in metric spaces. Discrete Comput. Geom. 44, 686\u2013705 (2010)","journal-title":"Discrete Comput. Geom."},{"unstructured":"Mulzer, W.: Minimum dilation triangulations for the regular n-gon. Master\u2019s thesis, Freie Universit\u00e4t Berlin (2004)","key":"40_CR17"},{"key":"40_CR18","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546884","volume-title":"Geometric Spanner Networks","author":"G Narasimhan","year":"2007","unstructured":"Narasimhan, G., Smid, M.: Geometric Spanner Networks. Cambridge University Press, Cambridge (2007)"},{"key":"40_CR19","doi-asserted-by":"publisher","first-page":"3","DOI":"10.1016\/j.tcs.2005.06.022","volume":"344","author":"CH Papadimitriou","year":"2005","unstructured":"Papadimitriou, C.H., Ratajczak, D.: On a conjecture related to geometric routing. Theor. Comput. Sci. 344, 3\u201314 (2005)","journal-title":"Theor. Comput. Sci."},{"key":"40_CR20","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1017\/S0305004100071875","volume":"115","author":"G Rote","year":"1994","unstructured":"Rote, G.: Curves with increasing chords. Math. Proc. Camb. Philos. Soc. 115, 1\u201312 (1994)","journal-title":"Math. Proc. Camb. Philos. Soc."},{"issue":"4","key":"40_CR21","doi-asserted-by":"publisher","first-page":"1620","DOI":"10.1137\/110832458","volume":"42","author":"G Xia","year":"2013","unstructured":"Xia, G.: The stretch factor of the Delaunay triangulation is less than 1.998. SIAM J. Comput. 42(4), 1620\u20131659 (2013)","journal-title":"SIAM J. Comput."}],"container-title":["Lecture Notes in Computer Science","Graph Drawing and Network Visualization"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-50106-2_40","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,13]],"date-time":"2025-06-13T07:55:50Z","timestamp":1749801350000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-319-50106-2_40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783319501055","9783319501062"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-50106-2_40","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"8 December 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"GD","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Symposium on Graph Drawing and Network Visualization","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Athens","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Greece","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2016","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 September 2016","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"21 September 2016","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"24","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"gd2016","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}