2,444 research outputs found
Two New Bounds on the Random-Edge Simplex Algorithm
We prove that the Random-Edge simplex algorithm requires an expected number
of at most 13n/sqrt(d) pivot steps on any simple d-polytope with n vertices.
This is the first nontrivial upper bound for general polytopes. We also
describe a refined analysis that potentially yields much better bounds for
specific classes of polytopes. As one application, we show that for
combinatorial d-cubes, the trivial upper bound of 2^d on the performance of
Random-Edge can asymptotically be improved by any desired polynomial factor in
d.Comment: 10 page
Building Efficient and Compact Data Structures for Simplicial Complexes
The Simplex Tree (ST) is a recently introduced data structure that can
represent abstract simplicial complexes of any dimension and allows efficient
implementation of a large range of basic operations on simplicial complexes. In
this paper, we show how to optimally compress the Simplex Tree while retaining
its functionalities. In addition, we propose two new data structures called the
Maximal Simplex Tree (MxST) and the Simplex Array List (SAL). We analyze the
compressed Simplex Tree, the Maximal Simplex Tree, and the Simplex Array List
under various settings.Comment: An extended abstract appeared in the proceedings of SoCG 201
FitSKIRT: genetic algorithms to automatically fit dusty galaxies with a Monte Carlo radiative transfer code
We present FitSKIRT, a method to efficiently fit radiative transfer models to
UV/optical images of dusty galaxies. These images have the advantage that they
have better spatial resolution compared to FIR/submm data. FitSKIRT uses the
GAlib genetic algorithm library to optimize the output of the SKIRT Monte Carlo
radiative transfer code. Genetic algorithms prove to be a valuable tool in
handling the multi- dimensional search space as well as the noise induced by
the random nature of the Monte Carlo radiative transfer code. FitSKIRT is
tested on artificial images of a simulated edge-on spiral galaxy, where we
gradually increase the number of fitted parameters. We find that we can recover
all model parameters, even if all 11 model parameters are left unconstrained.
Finally, we apply the FitSKIRT code to a V-band image of the edge-on spiral
galaxy NGC4013. This galaxy has been modeled previously by other authors using
different combinations of radiative transfer codes and optimization methods.
Given the different models and techniques and the complexity and degeneracies
in the parameter space, we find reasonable agreement between the different
models. We conclude that the FitSKIRT method allows comparison between
different models and geometries in a quantitative manner and minimizes the need
of human intervention and biasing. The high level of automation makes it an
ideal tool to use on larger sets of observed data.Comment: 14 pages, 10 figures; accepted for publication in Astronomy and
Astrophysic
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
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