The crust and the &Bgr;-Skeleton: combinatorial curve reconstruction
Graphical Models and Image Processing
Localized algorithms for energy efficient topology in wireless ad hoc networks
Proceedings of the 5th ACM international symposium on Mobile ad hoc networking and computing
Modeling and visualization of leaf venation patterns
ACM SIGGRAPH 2005 Papers
On the Longest Edge of Gabriel Graphs in Wireless Ad Hoc Networks
IEEE Transactions on Parallel and Distributed Systems
Bioevaluation of World Transport Networks
Bioevaluation of World Transport Networks
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A @b-skeleton, @b=1, is a planar proximity undirected graph of a Euclidean points set, where nodes are connected by an edge if their lune-based neighbourhood contains no other points of the given set. Parameter @b determines the size and shape of the lune-based neighbourhood. A @b-skeleton of a random planar set is usually a disconnected graph for @b2. With the increase of @b, the number of edges in the @b-skeleton of a random graph decreases. We show how to grow stable @b-skeletons, which are connected for any given value of @b and characterise morphological transformations of the skeletons governed by @b and a degree of approximation. We speculate how the results obtained can be applied in biology and chemistry.