T. H. Su and R. Ch. Chang. Computing the constrained relative neighborhood graphs and gabriel graphs in euclidean plane. Pattern Recogn., 24:221-230, 1991. 93  Home/Search   Document Not in Database   Summary   Related Articles   Check

....disconnects the tree into two trees T 1 and T 2 , with a 2 T 1 and b 2 T 2 . Since x was in T , it must be in one of the two components. Without loss of generality, let x 2 T 1 . Thus, the tree T = T e xb has lower weight than T contradicting the fact that T has minimum weight. Su and Chang [14] presented an algorithm to compute the constrained relative neighborhood graph of a set of disjoint line segments in O(n log n) time by pruning the constrained delaunay triangulation of the set. Since there are a linear number of edges in such a graph, we can then apply any o(n log n) time minimum ....

T. SU AND R. CHANG. Computing the constrained relative neighborhood graphs and constrained Gabriel graphs in Euclidean plane. Pattern Recognition, 24, 3, pp. 221-230, 1991.

....disconnects the tree into two trees T 1 and T 2 , with a 2 T 1 and b 2 T 2 . Since x was in T , it must be in one of the two components. Without loss of generality, let x 2 T 1 . Thus, the tree T = T e xb has lower weight than T contradicting the fact that T has minimum weight. Su and Chang [12] presented an algorithm to compute the constrained relative neighborhood graph of a set of disjoint line segments in O(n log n) time. Since there are a linear number of edges in such a graph, we can then apply any o(n log n) time minimum spanning tree algorithm ( 6] 13] to the resulting ....

T. Su and R. Chang. Computing the constrained relative neighborhood graphs and constrained Gabriel graphs in Euclidean plane. Pattern Recognition, 24, 3, pp. 221230, 1991.

....Gabriel graph. In this context, ElGindy and Toussaint [ET88] first addressed the problem of computing the relative neighborhood graph of a set of line segments where the line segments form a simple polygon. They presented an O(n ) time algorithm to compute this graph. Subsequently, Su and Chang [SC91] presented optimal O(n log n) time algorithms to compute both the constrained relative neighborhood graph and the constrained Gabriel graph by essentially pruning the constrained Delaunay triangulation. The main emphasis in the study of proximity graphs constrained to a set of line segments has ....

Tung-Hsin Su and Ruei-Chuan Chang. Computing the constrained relative neighborhood graphs and constrained gabriel graphs in Euclidean plane. Pattern Recogn. Lett., 24(3):221--230, 1991.

....edges including the constraining ones. This follows immediately from a constrained version of the Subgraph Theorem. In the Euclidean metric case, the problem can actually be solved in quadratic time because the relative neighborhood graph with constraining edges can be computed in O(n log n) time [SuCh91]. The question remains whether or not a min max length triangulation, with or without constraining edges, can be computed in less than quadratic time. The approach used by the solution is a version of the subgraph approach mentioned in Section 2.5. Both Plaisted and Hong [PlHo87] and Lingas ....

....paradigm. 83 Acknowledgments The results in this chapter are jointly developed by Herbert Edelsbrunner and myself [EdTa91] We thank Jerzy Jaromczyk (University of Kentucky) for pointing out various references on relative neighborhood graph, in particular, the paper by Su and Chang [SuCh91] that implies a quadratic time algorithm for the constrained min max length triangulation problem in the Euclidean case. 84 Chapter 6 Conforming Delaunay Triangulations A conforming Delaunay triangulation for a plane geometric graph G = S; E) is introduced in Section 1.2 as an extension to ....

T. H. Su and R. C. Chang. Computing the constrained relative neighborhood graphs and constrained Gabriel graphs in Euclidean plane. Pattern Recognition 24 (1991), 221--230.

....bottleneck matchings are discussed in [SC90] where an O(k 2 n log n) time construction for the k Gamma GG in R 2 is presented. Constrained relative neighborhood graphs and Gabriel graphs: An interesting extension of relative neighborhood graphs has been investigated by Su and Chang [SC91a] Let V be a set of n points in a plane and T be a set of nonintersecting line segments with their endpoints in V . Clearly, the number of segments in T is of order O(n) We say that two points in V are visible if their connecting line segment does not intersect any edge in T . The constrained ....

....special case of the CRNG, where T forms a simple polygon, was introduced much earlier in [ET88] Because of its applications to pattern recognition we will discuss this special case separately. It appears that CRNG(V [ T ) is a subgraph of the constrained Delaunay triangulation of V and T ; see [SC91a] The constrained Delaunay triangulation of V and T , CDT (V; T ) contains all segments in T . In addition, it includes all edges (p; q) such that p; q are visible and there is a sphere with its boundary containing p; q which does not contain points of V visible from both p and q. The CDT (V; T ....

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T.-H. Su and R.-Ch. Chang. Computing the constrained relative neighborhood graphs and constrained Gabriel graphs in Euclidean plane. Pattern Recognition, 24:221--230, 1991.

....the tree into two trees T 1 and T 2 , with a 2 T 1 and b 2 T 2 . Since x was in T , it must be in one of the two components. Without loss of generality, let x 2 T 1 . Thus, the tree T 0 = T Gamma e xb has lower weight than T contradicting the fact that T has minimum weight. Su and Chang [14] presented an algorithm to compute the constrained relative neighborhood graph of a set of disjoint line segments in O(n log n) time by pruning the constrained delaunay triangulation of the set. Since there are a linear number of edges in such a graph, we can then apply any o(n log n) time minimum ....

T. Su and R. Chang. Computing the constrained relative neighborhood graphs and constrained Gabriel graphs in Euclidean plane. Pattern Recognition, 24, 3, pp. 221-230, 1991.

....and p j are said to be visible if the line segment [p i , p j ] lies in P. It is an open question whether this decomposition can be computed in o(n 2 ) time and neither is a super linear lower bound known for this problem. However, under a slightly different visibility constraint Su and Chang [SC91a] are able to obtain an O(n log n) time algorithm for computing the RNG of a set of line segments. Clearly a simple polygon is a special case of a set of line segments and hence under their visibility constraint the RND of a simple polygon can be computed in O(n log n) time. Pankaj Agarwal has ....

T.-H. Su and R.-C. Chang, "Computing the constrained relative neighborhood graphs and constrained Gabriel graphs in Euclidean plane," Pattern Recognition, vol. 24, No. 3, 1991, pp. 221-230.

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T. H. Su and R. Ch. Chang. Computing the constrained relative neighborhood graphs and gabriel graphs in euclidean plane. Pattern Recogn., 24:221-230, 1991. 93

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T. Su and R. Chang, Computing the constrained relative neighborhood graphs and constrained Gabriel graphs in Euclidean plane. Pattern Recognition 24 (1991), 221-230.

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