A. Yao. On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM Journal on Computing, pages 721-- 736, 1982.  Home/Search Document Not in Database Summary Related Articles Check |
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Localized Delaunay Triangulation with Application in Ad.. - Li, Calinescu, Wan, Wang (2003) (Correct)
....u and v of V (H) ##H (u, v)####G (u, v)##t##H (u, v)#. With H understood, we also call t the length stretch factor of the spanner G. There are several geometrical structures which are proved to be t spanners for the Euclidean complete graph K(V ) of a point set V . For example, the Yao graph [21] and the # graph [22] have been shown to be t spanners. However, both these two geometrical structures are not guaranteed to be planar in two dimensions. Let #G (u, v) be the path found by a unicasting routing method # from node u to v in a weighted graph G, and (u, v)# be the length of the ....
....on t to be 2# 3cos 2.42. The best known lower bound on t is # 2, which is due to Chew [26] and it is widely believed to be the actual upper bound also. C. Proximity Graphs Besides the Delaunay triangulation, various proximity subgraphs of UDG can be defined [27] 28] 29] 30] [21] over a set of n two dimensional wireless nodes V . For convenience, let disk(u, v) be the closed disk with diameter uv, let disk(u, v , w) be the circumcircle defined by the triangle and let B(u, r) be the circle centered at u with radius r. Let x(v) and y(v) be the value of the x coordinate ....
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A. C.-C. Yao, "On constructing minimum spanning trees in k-dimensional spaces and related problems," SIAM J. Computing, vol. 11, pp. 721--736, 1982.
Localized Routing for Wireless Ad Hoc Networks - Li, Wang, Frieder (Correct)
....r n ) which has an edge uv iff the Euclidean distance #uv# between u and v is less than r n . We normalize r n to one unit if no confusion is caused. A. Proximity Graphs Various proximity graphs [18] e.g. relative neighborhood graph (RNG) 19] Gabriel graph (GG) 19] and Yao graph (YG) [20], were dened for UDG. Although Yao graph has constant spanning ratio [21] 22] 18] it is not planar. The relative neighborhood graph and the Gabriel graph are planar graphs, but they are not a spanner for the unit disk graph [12] Assume that no four nodes of V are co circular. A triangulation ....
A. C.-C. Yao, "On constructing minimum spanning trees in kdimensional spaces and related problems," SIAM J. Computing, vol. 11, pp. 721--736, 1982.
Linear-Size Approximate Voronoi Diagrams - Arya, Malamatos (2002) (2 citations) (Correct)
....we can easily show that, for any point q 2 b 1 , jqn x j (1 ffl) Delta NN q (S b 2 ) Thus (i) holds for R = fn x g. In the remainder we assume that fl 16=ffl. Let be a set of points on the boundary of b 3 that is ffi dense for the boundary, where ffi = r fflfl=16. By standard results [13], we can find such a set R of size ) For each point x 2 R , we let n x denote any point of S that is its (ffl=2) NN. We define g. We now show that R satisfies the property given in part (i) of the lemma. Let q be a point in b 1 . Let p denote the nearest neighbor of q among the points ....
A. C. Yao. On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM J. Comput., 11(4):721--736, 1982.
Sublinear-Time Approximation of Euclidean Minimum.. - Czumaj, Ergun.. (2003) (Correct)
....in dense graphs. In the simplest case where d = 2 (on the plane) Shamos and Hoey [29] show that the EMST problem can be solved in O(n log n) time. For d 3, no e O(n) time algorithm is known and it is a major open question whether an O(n log n) time algorithm exists even for d = 3 [17] Yao [32] was the first who broke the O(n ) time barrier for d 3 and designed an e O(n 1:8 ) time algorithm for d = 3. This bound has been later improved and the fastest currently known (randomized) algorithm achieves the running time of e O(n 4=3 ) 2] for d = 3 (and the running time tends to ....
....in the sense that one can use a different number of queries and obtain a whole range of tradeoffs between the running time and the quality of approximation. 4 Two related previous results We now describe two previous results that we utilize in our EMST algorithms: the concept of Yao graphs [32] and an algorithm for approximating the MST in bounded degree graphs due to Chazelle et al. 13] Yao graphs. Yao graphs are Euclidean graphs that relate the EMST to the cone nearest neighbor oracle presented in Section 2.1. Fix an integer d 2. Let C be a collection of d dimensional cones with ....
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A. C.-C. Yao. On constructing minimum spanning trees in k- dimensional spaces and related problems. SIAM Journal on Computing, 11(4):721--736, November 1982.
Distributed Construction of a Planar Spanner and Routing.. - Li, Calinescu, Wan (2002) (13 citations) (Correct)
....u and v of V (H) k H (u; v)k k G (u; v)k tk H (u; v)k. With H understood, we also call t the length stretch factor of the spanner G. There are several geometrical structures which are proved to be t spanners for the Euclidean complete graph K(S) of a point set S. For example, the Yao graph [16] and the graph [17] have been shown to be t spanners. However, both these two geometrical structures are not guaranteed to be planar in two dimensions. Given a set of points S, it is well known that the Delaunay triangulation Del(S) is a planar t spanner of the completed Euclidean graph K(S) ....
....to Chew [20] C. Proximity Graphs Let S be a set of n wireless nodes distributed in a twodimensional plane. These nodes induce a unit disk graph UDG(S) in which there is an edge uv if and only if kuvk 1. Various proximity subgraphs of the unit disk graph can be defined [21] 22] 23] 24] [16]. For convenience, let disk (u; v) be the closed disk with diameter uv, let disk (u; v; w) be the circumcircle defined by the triangle 4uvw, and let B(u; r) be the circle centered at u with radius r. Let x(v) and y(v) be the value of the x coordinate and y coordinate of a node v respectively. ....
[Article contains additional citation context not shown here]
A. C.-C. Yao, "On constructing minimum spanning trees in k-dimensional spaces and related problems," SIAM J. Computing, vol. 11, pp. 721--736, 1982.
Fault Tolerant Deployment and Topology Control in Wireless.. - Li, Wan, Wang (2003) (3 citations) (Correct)
....wireless ad hoc networks has draw considerable attentions recently [1, 13, 14, 15, 25, 26, 32] Topology control methods try to maintain a structure that can be used for efficient routing or improving the overall networking performance. Li et al. 14, 15, 32] had proposed to use the Yao structure [34] on the unit disk graph for topology control without sacrificing too much on the energy conservation. Yao structure does not provide fault tolerance. Recently, Bahramgiri et al. 1] proposed a fault tolerant topology control algorithm which shows how to decide the minimum transmission range of ....
....the power needed to support a link uv is , where is the Euclidean distance between u and v. Lukovszki [16] gave a method to construct a spanner that can sustain k nodes or links failures for complete graph. Our topology control method is based on this method and the following Yao structure [34]. The Yao graph over a (directed) graph G with an integer parameter p 6, denoted by # YG p (G) is defined as follows. At each node u,anyp equal separated rays originated at u define p equal cones. In each cone, choose the shortest (directed) edge uv G, if there is any, and add a directed ....
A. C.-C. Yao. On constructing minimum spanning trees in k-dimensional spaces and related problems. SIAM J. Computing, 11:721--736, 1982.
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