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| [[File:Yao graph.svg|thumb|right|200px]]
| | I'm Florrie and I live in Eindhoven. <br>I'm interested in Athletics and Physical Education, Creative writing and Portuguese art. I like to travel and watching Arrested Development.<br><br>Also visit my page; [https://www.youtube.com/watch?v=YV1eAKnnbSM&list=UUlzIDSeXWfrlcd2Eklh-y-g Hockey Training Program] |
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| In [[computational geometry]], the '''Yao graph''', named after [[Andrew Yao]], is a kind of [[geometric spanner]], a weighted [[undirected graph]] connecting a set of [[point (geometry)|geometric points]] with the property that, for every pair of points in the graph, their [[shortest path]] has a length that is within a constant factor of their [[Euclidean distance]].
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| The basic idea underlying the two-dimensional Yao graph is to surround each of the given points by equally spaced [[ray (geometry)|rays]], partitioning the plane into sectors with equal angles, and to connect each point to its [[nearest neighbor]] in each of these sectors.<ref>{{cite web|title=Overlay Networks for Wireless Systems|url=http://www.cs.jhu.edu/~scheideler/courses/600.348_F04/lecture_13.pdf}}</ref> Associated with a Yao graph is an integer parameter {{math|''k'' ≥ 6}} which is the number of rays and sectors described above; larger values of {{math|''k''}} produce closer approximations to the Euclidean distance.<ref>{{cite web|title=Simple Topologies|url=http://www.cs.kent.edu/~dfuhry/presentations/simple_topologies.pdf}}</ref> The stretch factor is at most <math>1/(\cos \theta - \sin \theta)</math>, where <math>\theta</math> is the angle of the sectors.<ref name=YaoPaper /> The same idea can be extended to point sets in more than two dimensions, but the number of sectors required grows exponentially with the dimension.
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| [[Andrew Yao]] used these graphs to construct high-dimensional [[Euclidean minimum spanning tree]]s.<ref name="YaoPaper">{{citation|first=A. C.|last=Yao|authorlink=Andrew Yao|title=On constructing minimum spanning trees in ''k''-dimensional space and related problems|journal=[[SIAM Journal on Computing]]|volume=11|year=1982|pages=721–736|issue=4|doi=10.1137/0211059}}.</ref>
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| ==See also==
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| * [[Theta graph]]
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| ==References==
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| {{Reflist}}
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| {{DEFAULTSORT:Yao Graph}}
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| [[Category:Computational geometry]]
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| [[Category:Geometric graph theory]]
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Latest revision as of 17:29, 30 July 2014
I'm Florrie and I live in Eindhoven.
I'm interested in Athletics and Physical Education, Creative writing and Portuguese art. I like to travel and watching Arrested Development.
Also visit my page; Hockey Training Program