Dense point sets have sparse Delaunay triangulations

The spread of a finite set of points is the ratio between the longest and shortest pairwise distances. We prove that the Delaunay triangulation of any set of n points in R^3 with spread D has complexity O(D^3). This bound is tight in the worst case for all D = O(sqrt{n}). In particular, the Delaunay triangulation of any dense point set has linear complexity. We also generalize this upper bound to regular triangulations of k-ply systems of balls, unions of several dense point sets, and uniform samples of smooth surfaces. On the other hand, for any n and D=O(n), we construct a regular triangulation of complexity Omega(nD) whose n vertices have spread D.Comment: 31 pages, 11 figures. Full version of SODA 2002 paper. Also available at http://www.cs.uiuc.edu/~jeffe/pubs/screw.htm

08171 Abstracts Collection -- Beyond the Finite: New Challenges in Verification and Semistructured Data

From 20.04. to 25.04.2008, the Dagstuhl Seminar 08171 ``Beyond the Finite: New Challenges in Verification and Semistructured Data\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available

Optimization and scalability of tiled code generation

PIPS is a source-to-source compiler developed by CRI ParisTech performing loop tiling to enforce locality and parallelism.In this work we designed a new PIPS phase performing an invariant code optimization and parallel directive selection on the generated tiled code.We obtained scalable tiled code and minimized the parallel directive overhead.The current PIPS generated code outperforms the previous one and achieves comparable results to other state-of-art code optimizers in terms of speed-up.ope

An approach to three-dimensional scene databases

technical reportCurrent image database research is concerned for the most part with the encoding and processing of two-dimensional images. However, the most successful approach to computer vision is based on 3-dimensional information, organized as either stacks of 2-D images (e.g., the intrinsic images of Barrow and Tennenbaum, or the 2 1/2 dimensional sketch of Marr) or as actual 3-dimensional data (e.g., the Multisensor Kernel System of Henderson). Efficient techniques for two-dimensional image processing have been well-developed over the last few decades and special purpose architectures are now available. However, the study of the organization, processing and analysis of three-dimensional scene data is only just beginning. We describe one approach to the representation of three-dimensional image data and evaluate several computer vision algorithms performed on the data. Finally, we describe how three-dimensional feature operations can be performed as relational database operations

Aspects of Unstructured Grids and Finite-Volume Solvers for the Euler and Navier-Stokes Equations

One of the major achievements in engineering science has been the development of computer algorithms for solving nonlinear differential equations such as the Navier-Stokes equations. In the past, limited computer resources have motivated the development of efficient numerical schemes in computational fluid dynamics (CFD) utilizing structured meshes. The use of structured meshes greatly simplifies the implementation of CFD algorithms on conventional computers. Unstructured grids on the other hand offer an alternative to modeling complex geometries. Unstructured meshes have irregular connectivity and usually contain combinations of triangles, quadrilaterals, tetrahedra, and hexahedra. The generation and use of unstructured grids poses new challenges in CFD. The purpose of this note is to present recent developments in the unstructured grid generation and flow solution technology