Single-step creation of localized Delaunay triangulations

Single-step creation of localized Delaunay triangulations

A localized Delaunay triangulation owns the following interesting properties for sensor and wireless ad hoc networks: it can be built with localized information, the communication cost imposed by control information is limited, and it supports geographical routing algorithms that offer guaranteed convergence. This paper presents two localized algorithms, FLDT1 and FLDT2, that build a graph call...

Restricted Constrained Delaunay Triangulations

We introduce the restricted constrained Delaunay triangulation (restricted CDT). The restricted CDT generalizes the restricted Delaunay triangulation, allowing us to define a triangulation of a surface that includes a set of constraining segments. Under certain sampling conditions, the restricted CDT includes every constrained segment and suggests an algorithm that produces a triangulation of t...

Blocking Delaunay triangulations

Given a set B of n black points in general position, we say that a set of white points W blocks B if in the Delaunay triangulation of [Formula: see text] there is no edge connecting two black points. We give the following bounds for the size of the smallest set W blocking B: (i) [Formula: see text] white points are always sufficient to block a set of n black points, (ii) if B is in convex posit...

Higher Order Delaunay Triangulations

Dynamic Maintenance of Delaunay Triangulations

We describe and analyze the complexity of a procedure for computing and updating a Delaunay triangulation of a set of points in the plane subject to incremental insertions and deletions. Our method is based on a recent algo rithm of Guibas, Knuth, and Sharir for constructing Delaunay triangulations by incremental point insertion only. Our implementation features several meth ods that are not us...