This paper presents an algorithm for obtaining a constrained Delaunay triangulation from a given planar graph. The main advantage towards other algorithms is that I use an efficient Žalik’s algorithm, using a plane subdivison for obtaining a Delaunay triangulation. It is used for insertion of points into existing triangulation. The other part of algorithm presents a method for inserting edges, ...

In this paper, a methodology for modeling surface wildfire propagation through a complex landscape is presented. The methodology utilizes a Delaunay triangulation to represent surface fire spread within the landscape. A procedure to construct the graph and estimate the rate of spread along the edges of a network is discussed. After the Delaunay data structure is constructed, a two pass shortest...

We consider geometric hypergraphs whose vertex set is a finite of points (e.g., in the plane), and hyperedges are intersections this with family regions axis-parallel rectangles). A typical coloring problem for such asks, given an integer k, existence m=m(k), that every can be k-colored hyperedge size at least m contains different (or all k) colors. generalize notion by introducing t-subsets en...

We generalize β-skeletons, well-known neighborhood graphs for point sets, to sets of line segments and present algorithms for computing such skeletons, both circle and lens-based, for the entire range of β values. In particular, for β ≥ 1 the β-skeleton for a set S on n segments in the Euclidean plane can be constructed in O(nα(n) log n) time and the construction relies on the Delaunay triangul...

Minimum spanning tree problem is a very important problem in VLSI CAD. Given n points in a plane, a minimum spanning tree is a set of edges which connects all the points and has a minimum total length. A naive approach enumerates edges on all pairs of points and takes at least (n 2) time. More eecient approaches nd a minimum spanning tree only among edges in the Delaunay triangulation of the po...

Given a plane forest F = (V,E) of |V | = n points, we find the minimum set S ⊆ E of edges such that the edge-constrained minimum spanning tree over the set V of vertices and the set S of constraints contains F . We present an O(n logn)-time algorithm that solves this problem. We generalize this to other proximity graphs in the constraint setting, such as the relative neighbourhood graph, Gabrie...

Abstrac t . A graph is minimum weight drawable if it admits a straightline drawing that is a minimum weight triangulation of the set of points representing the vertices of the graph. In this paper we consider the problem of characterizing those graphs that are minimum weight draw~ble. Our contribution is twofold: We show that there exist infinitely many triangulations that are not minimum weigh...

Finding recurring structural features among proteins three-dimensional (3D) structures is an important problem in bioinformatics. In this paper we apply a novel subgraph mining algorithm to three related graph representations of the sequence and proximity characteristics of a protein’s amino acid residues. The subgraph mining algorithm is used to discover spatial motifs that can be used to disc...

The relative neighbourhood graph (RNG) of a set of n points on the plane is defined. The ability of the RNG to extract a perceptually meaningful structure from the set of points is briefly discussed and compared to that of two other graph structures: the minimal spanning tree (MST) and the Delaunay (Voronoi) triangulation (DT). It is shown that the RNG is a superset of the MST and a subset of t...

Let G = G(n, r) be a random geometric graph resulting from placing n nodes uniformly at random in the unit square (disk) and connecting every two nodes if and only if their Euclidean distance is at most r . Let rcon = q logn πn be the known critical radius guaranteeing connectivity when n → ∞. The Restricted Delaunay Graph RDG(G) is a subgraph of G with the following properties: it is a planar ...