Delaunay graphs are almost as good as complete graphs
Delaunay graphs are almost as good as complete graphs
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DOI：
10.1109/sfcs.1987.18
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发表时间：
1987-10
影响因子：
0.8
通讯作者：
D. Dobkin;Steven J. Friedman;K. Supowit
中科院分区：
文献类型：
--
作者：
D. Dobkin;Steven J. Friedman;K. Supowit
设S是平面上任意N个点的集合，DT（S）是S的Delaunay三角剖分图。对于S中的所有点sa和B，设d（a，B）为从a到B的欧氏距离，DT（a，B）为DT（S）中从a到B的最短路的长度.证明了存在一个与S和N无关的常数tc（≤（（1 + π 5）/2）π <$5.08），使得% MathType! MTEF!二号! 1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL 2x9gzLbvyNv2CaerbuLwBLn%hiov2DGi1BTfMBaeXatLxBI9gBa erbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaibe@abeqaamaabaabaaGcbaWaaSaaaaaie % aacaWFebGaa8hvaiaa-HcacaWGHbGaaiilaaadkgacaWFPaaabaGa % amizaiaaa-你好!四二四八! $$\frac {{DT（a，B）}}{{d（a，B）}}<c.$$
AbstractLetS be any set ofN points in the plane and let DT(S) be the graph of the Delaunay triangulation ofS. For all pointsa andb ofS, letd(a, b) be the Euclidean distance froma tob and let DT(a, b) be the length of the shortest path in DT(S) froma tob. We show that there is a constantc (≤((1+√5)/2) π≈5.08) independent ofS andN such that % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVy0de9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaaSaaaeaaie% aacaWFebGaa8hvaiaa-HcacaWGHbGaaiilaiaadkgacaWFPaaabaGa% amizaiaa-HcacaWGHbGaaiilaiaadkgacaWFPaaaaiabgYda8iaado% gacaGGUaaaaa!4248! $$\frac{{DT(a,b)}}{{d(a,b)}}< c.$$