{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T11:24:19Z","timestamp":1760441059510},"reference-count":5,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Math. Algorithm. Appl."],"published-print":{"date-parts":[[2012,6]]},"abstract":"<jats:p> Yao and Theta graphs are defined for a given point set and a fixed integer k &gt; 0. The space around each point is divided into k cones of equal angle, and each point is connected to a nearest neighbor in each cone. The difference between Yao and Theta graphs is in the way the nearest neighbor is defined: Yao graphs minimize the Euclidean distance between a point and its neighbor, and Theta graphs minimize the Euclidean distance between a point and the orthogonal projection of its neighbor on the bisector of the hosting cone. We prove that, corresponding to each edge of the Theta graph \u0398<jats:sub>6<\/jats:sub>, there is a path in the Yao graph Y<jats:sub>6<\/jats:sub> whose length is at most 8.82 times the edge length. Combined with the result of Bonichon et al., who prove an upper bound of 2 on the stretch factor of \u0398<jats:sub>6<\/jats:sub>, we obtain an upper bound of 17.64 on the stretch factor of Y<jats:sub>6<\/jats:sub>. <\/jats:p>","DOI":"10.1142\/s1793830912500243","type":"journal-article","created":{"date-parts":[[2012,6,19]],"date-time":"2012-06-19T10:55:53Z","timestamp":1340103353000},"page":"1250024","source":"Crossref","is-referenced-by-count":6,"title":["YAO GRAPHS SPAN THETA GRAPHS"],"prefix":"10.1142","volume":"04","author":[{"given":"MIRELA","family":"DAMIAN","sequence":"first","affiliation":[{"name":"Department of Computer Science, Villanova University, Villanova, USA"}]},{"given":"KRISTIN","family":"RAUDONIS","sequence":"additional","affiliation":[{"name":"Department of Computer Science, Villanova University, Villanova, USA"}]}],"member":"219","published-online":{"date-parts":[[2012,6,21]]},"reference":[{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1016\/j.comgeo.2004.04.003"},{"key":"rf5","unstructured":"B.\u00a0Hamdaoui and P.\u00a0Ramanathan, Sensor Network Operations (Wiley-IEEE Press, 2006)\u00a0pp. 291\u2013308."},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511546884"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.1016\/0022-0000(89)90044-5"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719772"}],"container-title":["Discrete Mathematics, Algorithms and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S1793830912500243","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T18:42:13Z","timestamp":1565116933000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S1793830912500243"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,6]]},"references-count":5,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2012,6,21]]},"published-print":{"date-parts":[[2012,6]]}},"alternative-id":["10.1142\/S1793830912500243"],"URL":"https:\/\/doi.org\/10.1142\/s1793830912500243","relation":{},"ISSN":["1793-8309","1793-8317"],"issn-type":[{"value":"1793-8309","type":"print"},{"value":"1793-8317","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,6]]}}}