protein structural flexibility is important for catalysis, binding, protein design, and allostery. some simple methods have recently been introduced to compute protein flexibility directly from the protein structure without any mechanical models. for example the atomic mean square displacement (or b-factor) is related to the number of neighboring atoms. the protein structure can be modeled as a...

Θk-graphs are geometric graphs that appear in the context of graph navigation. The shortest-path metric of these graphs is known to approximate the Euclidean complete graph up to a factor depending on the cone number k and the dimension of the space. TD-Delaunay graphs, a.k.a. triangular-distance Delaunay triangulations introduced by Chew, have been shown to be plane 2-spanners of the 2D Euclid...

Given a set P of n points in the plane, the order-k Delaunay graph is a graph with vertex set P and an edge exists between two points p, q ∈ P when there is a circle through p and q with at most k other points of P in its interior. We provide upper and lower bounds on the number of edges in an order-k Delaunay graph. We study the combinatorial structure of the set of triangulations that can be ...

A wireless sensor network can be represented by a graph. While the network graph is extremely useful, it often exhibits undesired irregularity. Therefore, special treatment of the graph is required by a variety of network algorithms and protocols. In particular, many geometry-oriented algorithms depend on a type of subgraph called Delaunay triangulation. However, when location information is un...

We introduce the notion of generalized Delaunay triangulation of a planar straight-line graph G = (V, E) in the Euclidean plane and present some characterizations of the triangulation. It is shown that the generalized Delaunay triangulation has the property that the minimum angle of the triangles in the triangulation is maximum among all possible triangulations of the graph. A general algorithm...

In this paper we study proximity structures like Delaunay triangulations based on geometric graphs, i.e. graphs which are subgraphs of the complete geometric graph. Given an arbitrary geometric graph G, we define several Voronoi diagrams, Delaunay triangulations, relative neighborhood graphs, Gabriel graphs and then study their complexities when G is a general geometric graph or G is some speci...

In this paper, we give the definition for the voronoi diagram and its dual graph – Delaunay triangulation for 3D cuboids. We prove properties of the 3D Delaunay triangulation, and provide algorithms to construct and update the Delaunay triangulation. The Delaunay triangulation data structure is used to perform proximity searches for both static and kinetic cases. We describe experimental result...

Geometric spanners can be used for efficient routing in wireless ad hoc networks. Computation of existing spanners for ad hoc networks primarily focused on geometric properties without considering network requirements. In this paper we propose a new spanner called Constrained Delaunay Triangulation (CDT) which considers both geometric properties and network requirements. The CDT is formed by in...

This paper proposed a new spectral graph clustering model by casting the non-categorical spatial data sets into an undirected graph. Decomposition of the graph to Delaunay graph has been done for computational efficiency. All pair shortest path based model has been adapted for the creation of the underlying Laplacian matrix of the graph. The similarity among the nodes of the graph is measured b...

In the pursuit of realistic terrain models, Gudmundsson, Hammar, and van Kreveld introduced higher-order Delaunay triangulations. A usual Delaunay triangulation is a 0order Delaunay triangulation, thus unique for a non-degenerate point set, while order-k Delaunay triangulations can be non-unique when k ≥ 1. In this work, we propose an algorithm to list all order-k Delaunay triangulations of a g...