Consider the following heuristic for planar Euclidean instances of the traveling salesman problem (TSP): select a subset of the edges which induces a planar graph, and solve either the TSP or its graphical relaxation on that graph. In this paper, we give several motivations for considering this heuristic, along with extensive computational results. It turns out that the Delaunay and greedy tria...

Discovering the topology of a set of labeled data in a Euclidian space can help to design better decision systems. In this work, we propose a supervised generative model based on the Delaunay Graph of some prototypes representing the labeled data.

We study a new family of geometric graphs that interpolate between the Delaunay triangulation and the Gabriel graph. These graphs share many properties with βskeletons for β ∈ [0, 1] (such as sublinear spanning ratio) with the added benefit of planarity (and consequently linear size and local routability).

Two-dimensional constrained Delaunay triangulations (of a planar straight-linegraph) introduced independently by Lee et al. [2] and Chew [1] are well studied struc-tures and can be constructed in optimal time. However, the generalization of suchobjects to three and higher dimensions is much less discussed in literature.In this talk, we first define a constrained Delaunay tri...

In this paper, we present a fully automatic Delaunay based sculpting algorithm for approximating the shape of a finite set of points S in R2. The algorithm generates a relaxed Gabriel graph (RGG) that consists of most of the Gabriel edges and a few non-Gabriel edges induced by the Delaunay triangulation. Holes are characterized through a structural pattern called as body-arm formed by the Delau...

This paper introduces a two-level approach for image segmentation based on region and edge integration. Edges are first detected in the original image using a combination of operators for intensity gradient and texture discontinuities. To preserve the spatial coherence of the edges and their surrounding image regions, the detected edges are vectorized into connected line segments which serve as...

Given a point configuration A, we uncover connection between polynomial-reproducing spline spaces over subsets of conv(A) and fine zonotopal tilings the zonotope Z(V) associated to corresponding vector configuration. This link directly generalizes known result on Delaunay configurations naturally encompasses, due its combinatorial character, case repeated affinely dependent points in A. We prov...

Iso-surfaces are routinely used for the visualization of volumetric structures. Further processing (such as quantitative analysis, morphometric measurements, shape description) requires volume representations. The skeleton representation matches these requirements by providing a concise description of the object. This paper has two parts. First, we exhibit an algorithm which locally builds an i...

We consider the problem of constructing bounded-degree planar geometric spanners of Euclidean and unit-disk graphs. It is well known that the Delaunay subgraph is a planar geometric spanner with stretch factor Cdel ≈ 2.42; however, its degree may not be bounded. Our first result is a very simple linear time algorithm for constructing a subgraph of the Delaunay graph with stretch factor ρ = 1 + ...

We consider the question: “What is the smallest degree that can be achieved for a plane spanner of a Euclidean graph E?” The best known bound on the degree is 14. We show that E always contains a plane spanner of maximum degree 6 and stretch factor 6. This spanner can be constructed efficiently in linear time given the Triangular Distance Delaunay triangulation introduced by Chew.