{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,25]],"date-time":"2025-03-25T20:49:51Z","timestamp":1742935791789,"version":"3.40.3"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"type":"print","value":"9783030835071"},{"type":"electronic","value":"9783030835088"}],"license":[{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,1,1]],"date-time":"2021-01-01T00:00:00Z","timestamp":1609459200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021]]},"DOI":"10.1007\/978-3-030-83508-8_1","type":"book-chapter","created":{"date-parts":[[2021,7,30]],"date-time":"2021-07-30T13:05:06Z","timestamp":1627650306000},"page":"1-14","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the Spanning and Routing Ratios of the Directed $$\\varTheta _6$$-Graph"],"prefix":"10.1007","author":[{"given":"Hugo A.","family":"Akitaya","sequence":"first","affiliation":[]},{"given":"Ahmad","family":"Biniaz","sequence":"additional","affiliation":[]},{"given":"Prosenjit","family":"Bose","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,7,31]]},"reference":[{"issue":"9","key":"1_CR1","doi-asserted-by":"publisher","first-page":"910","DOI":"10.1016\/j.comgeo.2014.05.001","volume":"47","author":"O Aichholzer","year":"2014","unstructured":"Aichholzer, O., et al.: Theta-3 is connected. Comput. Geom.: Theory Appl. 47(9), 910\u2013917 (2014)","journal-title":"Comput. Geom.: Theory Appl."},{"key":"1_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1007\/978-3-642-40104-6_10","volume-title":"Algorithms and Data Structures","author":"L Barba","year":"2013","unstructured":"Barba, L., Bose, P., De Carufel, J.L., van Renssen, A., Verdonschot, S.: On the stretch factor of the theta-4 graph. In: Dehne, F., Solis-Oba, R., Sack, J.R. (eds.) Algorithms and Data Structures. LNCS, vol. 8037, pp. 109\u2013120. Springer, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40104-6_10"},{"doi-asserted-by":"crossref","unstructured":"Bonichon, N., Bose, P., Carmi, P., Kostitsyna, I., Lubiw, A., Verdonschot, S.: Gabriel triangulations and angle-monotone graphs: local routing and recognition. In: International Symposium on Graph Drawing and Network Visualization, pp. 519\u2013531. Springer, Heidelberg (2016)","key":"1_CR3","DOI":"10.1007\/978-3-319-50106-2_40"},{"key":"1_CR4","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.) Graph Theoretic Concepts in Computer Science. LNCS, vol. 6410, pp. 266\u2013278. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-16926-7_25"},{"unstructured":"Bose, P., De Carufel, J.-L., Devillers, O.: Expected complexity of routing in $$\\Theta _6$$ and half-$$\\Theta _6$$ graphs. arXiv preprint arXiv:1910.14289 (2019)","key":"1_CR5"},{"doi-asserted-by":"crossref","unstructured":"Bose, P., De Carufel, J.-L., Hill, D., Smid, M.H.M.: On the spanning and routing ratio of Theta-four. In: Symposium on Discrete Algorithms, pp. 2361\u20132370. SIAM (2019)","key":"1_CR6","DOI":"10.1137\/1.9781611975482.144"},{"key":"1_CR7","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1016\/j.tcs.2015.12.017","volume":"616","author":"P Bose","year":"2016","unstructured":"Bose, P., De Carufel, J.-L., Morin, P., van Renssen, A., Verdonschot, S.: Towards tight bounds on theta-graphs: more is not always better. Theoret. Comput. Sci. 616, 70\u201393 (2016)","journal-title":"Theoret. Comput. Sci."},{"issue":"6","key":"1_CR8","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."},{"issue":"4","key":"1_CR9","doi-asserted-by":"publisher","first-page":"937","DOI":"10.1137\/S0097539700369387","volume":"33","author":"P Bose","year":"2004","unstructured":"Bose, P., Morin, P.: Online routing in triangulations. SIAM J. Comput. 33(4), 937\u2013951 (2004)","journal-title":"SIAM J. Comput."},{"issue":"2","key":"1_CR10","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1016\/0022-0000(89)90044-5","volume":"39","author":"P Chew","year":"1989","unstructured":"Chew, 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."},{"doi-asserted-by":"crossref","unstructured":"Clarkson, K.: Approximation algorithms for shortest path motion planning. In: Proceedings of the 19th Annual ACM Symposium on Theory of Computing (STOC 1987), pp. 56\u201365 (1987)","key":"1_CR11","DOI":"10.1145\/28395.28402"},{"key":"1_CR12","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1007\/BF01386390","volume":"1","author":"E Dijkstra","year":"1959","unstructured":"Dijkstra, E.: A note on two problems in connexion with graphs. Numer. Math. 1, 269\u2013271 (1959)","journal-title":"Numer. Math."},{"doi-asserted-by":"crossref","unstructured":"Eppstein, D.: Spanning trees and spanners. In: Handbook of Computational Geometry, pp. 425\u2013461 (1999)","key":"1_CR13","DOI":"10.1016\/B978-044482537-7\/50010-3"},{"key":"1_CR14","doi-asserted-by":"publisher","DOI":"10.1017\/9781108528986","volume-title":"Probability on Graphs: Random Processes on Graphs and Lattices","author":"G Grimmett","year":"2018","unstructured":"Grimmett, G.: Probability on Graphs: Random Processes on Graphs and Lattices, 2nd edn. Cambridge University Press, Cambridge (2018)","edition":"2"},{"issue":"6","key":"1_CR15","doi-asserted-by":"publisher","first-page":"372","DOI":"10.1145\/362248.362272","volume":"16","author":"J Hopcroft","year":"1973","unstructured":"Hopcroft, J., Tarjan, R.: Algorithm 447: efficient algorithms for graph manipulation. Commun. ACM 16(6), 372\u2013378 (1973)","journal-title":"Commun. ACM"},{"key":"1_CR16","doi-asserted-by":"publisher","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. Discret. Comput. Geom. 7, 13\u201328 (1992). https:\/\/doi.org\/10.1007\/BF02187821","journal-title":"Discret. Comput. Geom."},{"issue":"3","key":"1_CR17","doi-asserted-by":"publisher","first-page":"346","DOI":"10.1109\/TEC.1961.5219222","volume":"EC\u201310","author":"CY Lee","year":"1961","unstructured":"Lee, C.Y.: An algorithm for path connection and its applications. IRE Trans. Electron. Comput. EC\u201310(3), 346\u2013365 (1961)","journal-title":"IRE Trans. Electron. Comput."},{"key":"1_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":"1_CR19","doi-asserted-by":"publisher","first-page":"294","DOI":"10.1038\/072294b0","volume":"72","author":"K Pearson","year":"1865","unstructured":"Pearson, K.: The problem of the random walk. Nature 72, 294 (1865)","journal-title":"Nature"},{"unstructured":"Ruppert, J., Seidel, R.: Approximating the d-dimensional complete Euclidean graph. In: Proceedings of the 3rd Canadian Conference on Computational Geometry (CCCG 1991), pp. 207\u2013210 (1991)","key":"1_CR20"}],"container-title":["Lecture Notes in Computer Science","Algorithms and Data Structures"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-030-83508-8_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T11:25:11Z","timestamp":1645183511000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-030-83508-8_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021]]},"ISBN":["9783030835071","9783030835088"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-030-83508-8_1","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2021]]},"assertion":[{"value":"31 July 2021","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"WADS","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Workshop on Algorithms and Data Structures","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2021","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"9 August 2021","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"11 August 2021","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"wads2021","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"https:\/\/projects.cs.dal.ca\/wads2021\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Single-blind","order":1,"name":"type","label":"Type","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"EasyChair","order":2,"name":"conference_management_system","label":"Conference Management System","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"123","order":3,"name":"number_of_submissions_sent_for_review","label":"Number of Submissions Sent for Review","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"47","order":4,"name":"number_of_full_papers_accepted","label":"Number of Full Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"0","order":5,"name":"number_of_short_papers_accepted","label":"Number of Short Papers Accepted","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"38% - The value is computed by the equation \"Number of Full Papers Accepted \/ Number of Submissions Sent for Review * 100\" and then rounded to a whole number.","order":6,"name":"acceptance_rate_of_full_papers","label":"Acceptance Rate of Full Papers","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"3.1","order":7,"name":"average_number_of_reviews_per_paper","label":"Average Number of Reviews per Paper","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"13","order":8,"name":"average_number_of_papers_per_reviewer","label":"Average Number of Papers per Reviewer","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}},{"value":"Yes","order":9,"name":"external_reviewers_involved","label":"External Reviewers Involved","group":{"name":"ConfEventPeerReviewInformation","label":"Peer Review Information (provided by the conference organizers)"}}]}}