10 research outputs found
Convex Hull Formation for Programmable Matter
We envision programmable matter as a system of nano-scale agents (called
particles) with very limited computational capabilities that move and compute
collectively to achieve a desired goal. We use the geometric amoebot model as
our computational framework, which assumes particles move on the triangular
lattice. Motivated by the problem of sealing an object using minimal resources,
we show how a particle system can self-organize to form an object's convex
hull. We give a distributed, local algorithm for convex hull formation and
prove that it runs in asynchronous rounds, where is the
length of the object's boundary. Within the same asymptotic runtime, this
algorithm can be extended to also form the object's (weak) -hull,
which uses the same number of particles but minimizes the area enclosed by the
hull. Our algorithms are the first to compute convex hulls with distributed
entities that have strictly local sensing, constant-size memory, and no shared
sense of orientation or coordinates. Ours is also the first distributed
approach to computing restricted-orientation convex hulls. This approach
involves coordinating particles as distributed memory; thus, as a supporting
but independent result, we present and analyze an algorithm for organizing
particles with constant-size memory as distributed binary counters that
efficiently support increments, decrements, and zero-tests --- even as the
particles move
Algorithm Libraries for Multi-Core Processors
By providing parallelized versions of established algorithm libraries, we ease the exploitation of the multiple cores on modern processors for the programmer. The Multi-Core STL provides basic algorithms for internal memory, while the parallelized STXXL enables multi-core acceleration for algorithms on large data sets stored on disk. Some parallelized geometric algorithms are introduced into CGAL. Further, we design and implement sorting algorithms for huge data in distributed external memory
The projector algorithm: a simple parallel algorithm for computing Voronoi diagrams and Delaunay graphs
The Voronoi diagram is a certain geometric data structure which has numerous
applications in various scientific and technological fields. The theory of
algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich
and useful, with several different and important algorithms. However, this
theory has been quite steady during the last few decades in the sense that no
essentially new algorithms have entered the game. In addition, most of the
known algorithms are serial in nature and hence cast inherent difficulties on
the possibility to compute the diagram in parallel. In this paper we present
the projector algorithm: a new and simple algorithm which enables the
(combinatorial) computation of 2D Voronoi diagrams. The algorithm is
significantly different from previous ones and some of the involved concepts in
it are in the spirit of linear programming and optics. Parallel implementation
is naturally supported since each Voronoi cell can be computed independently of
the other cells. A new combinatorial structure for representing the cells (and
any convex polytope) is described along the way and the computation of the
induced Delaunay graph is obtained almost automatically.Comment: This is a major revision; re-organization and better presentation of
some parts; correction of several inaccuracies; improvement of some proofs
and figures; added references; modification of the title; the paper is long
but more than half of it is composed of proofs and references: it is
sufficient to look at pages 5, 7--11 in order to understand the algorith
Abstracts for the twentyfirst European workshop on Computational geometry, Technische Universiteit Eindhoven, The Netherlands, March 9-11, 2005
This volume contains abstracts of the papers presented at the 21st European Workshop on Computational Geometry, held at TU Eindhoven (the Netherlands) on March 9–11, 2005. There were 53 papers presented at the Workshop, covering a wide range of topics. This record number shows that the field of computational geometry is very much alive in Europe. We wish to thank all the authors who submitted papers and presented their work at the workshop. We believe that this has lead to a collection of very interesting abstracts that are both enjoyable and informative for the reader. Finally, we are grateful to TU Eindhoven for their support in organizing the workshop and to the Netherlands Organisation for Scientific Research (NWO) for sponsoring the workshop
Summary of Research 1994
The views expressed in this report are those of the authors and do not reflect the
official policy or position of the Department of Defense or the U.S. Government.This report contains 359 summaries of research projects which were carried out
under funding of the Naval Postgraduate School Research Program. A list of recent
publications is also included which consists of conference presentations and
publications, books, contributions to books, published journal papers, and
technical reports. The research was conducted in the areas of Aeronautics and
Astronautics, Computer Science, Electrical and Computer Engineering, Mathematics,
Mechanical Engineering, Meteorology, National Security Affairs, Oceanography,
Operations Research, Physics, and Systems Management. This also includes research
by the Command, Control and Communications (C3) Academic Group, Electronic Warfare
Academic Group, Space Systems Academic Group, and the Undersea Warfare Academic
Group