1,827 research outputs found
Space-Time Trade-offs for Stack-Based Algorithms
In memory-constrained algorithms we have read-only access to the input, and
the number of additional variables is limited. In this paper we introduce the
compressed stack technique, a method that allows to transform algorithms whose
space bottleneck is a stack into memory-constrained algorithms. Given an
algorithm \alg\ that runs in O(n) time using variables, we can
modify it so that it runs in time using a workspace of O(s)
variables (for any ) or time using variables (for any ). We also show how the technique
can be applied to solve various geometric problems, namely computing the convex
hull of a simple polygon, a triangulation of a monotone polygon, the shortest
path between two points inside a monotone polygon, 1-dimensional pyramid
approximation of a 1-dimensional vector, and the visibility profile of a point
inside a simple polygon. Our approach exceeds or matches the best-known results
for these problems in constant-workspace models (when they exist), and gives
the first trade-off between the size of the workspace and running time. To the
best of our knowledge, this is the first general framework for obtaining
memory-constrained algorithms
Problems on Polytopes, Their Groups, and Realizations
The paper gives a collection of open problems on abstract polytopes that were
either presented at the Polytopes Day in Calgary or motivated by discussions at
the preceding Workshop on Convex and Abstract Polytopes at the Banff
International Research Station in May 2005.Comment: 25 pages (Periodica Mathematica Hungarica, Special Issue on Discrete
Geometry, to appear
Addressing Integration Error for Polygonal Finite Elements Through Polynomial Projections: A Patch Test Connection
Polygonal finite elements generally do not pass the patch test as a result of
quadrature error in the evaluation of weak form integrals. In this work, we
examine the consequences of lack of polynomial consistency and show that it can
lead to a deterioration of convergence of the finite element solutions. We
propose a general remedy, inspired by techniques in the recent literature of
mimetic finite differences, for restoring consistency and thereby ensuring the
satisfaction of the patch test and recovering optimal rates of convergence. The
proposed approach, based on polynomial projections of the basis functions,
allows for the use of moderate number of integration points and brings the
computational cost of polygonal finite elements closer to that of the commonly
used linear triangles and bilinear quadrilaterals. Numerical studies of a
two-dimensional scalar diffusion problem accompany the theoretical
considerations
Parametric Inference for Biological Sequence Analysis
One of the major successes in computational biology has been the unification,
using the graphical model formalism, of a multitude of algorithms for
annotating and comparing biological sequences. Graphical models that have been
applied towards these problems include hidden Markov models for annotation,
tree models for phylogenetics, and pair hidden Markov models for alignment. A
single algorithm, the sum-product algorithm, solves many of the inference
problems associated with different statistical models. This paper introduces
the \emph{polytope propagation algorithm} for computing the Newton polytope of
an observation from a graphical model. This algorithm is a geometric version of
the sum-product algorithm and is used to analyze the parametric behavior of
maximum a posteriori inference calculations for graphical models.Comment: 15 pages, 4 figures. See also companion paper "Tropical Geometry of
Statistical Models" (q-bio.QM/0311009
Analysis domain model for shared virtual environments
The field of shared virtual environments, which also
encompasses online games and social 3D environments, has a
system landscape consisting of multiple solutions that share great functional overlap. However, there is little system interoperability between the different solutions. A shared virtual environment has an associated problem domain that is highly complex raising difficult challenges to the development process, starting with the architectural design of the underlying system. This paper has two main contributions. The first contribution is a broad domain analysis of shared virtual environments, which enables developers to have a better understanding of the whole rather than the part(s). The second contribution is a reference domain model for discussing and describing solutions - the Analysis Domain Model
VoroCrust: Voronoi Meshing Without Clipping
Polyhedral meshes are increasingly becoming an attractive option with
particular advantages over traditional meshes for certain applications. What
has been missing is a robust polyhedral meshing algorithm that can handle broad
classes of domains exhibiting arbitrarily curved boundaries and sharp features.
In addition, the power of primal-dual mesh pairs, exemplified by
Voronoi-Delaunay meshes, has been recognized as an important ingredient in
numerous formulations. The VoroCrust algorithm is the first provably-correct
algorithm for conforming polyhedral Voronoi meshing for non-convex and
non-manifold domains with guarantees on the quality of both surface and volume
elements. A robust refinement process estimates a suitable sizing field that
enables the careful placement of Voronoi seeds across the surface circumventing
the need for clipping and avoiding its many drawbacks. The algorithm has the
flexibility of filling the interior by either structured or random samples,
while preserving all sharp features in the output mesh. We demonstrate the
capabilities of the algorithm on a variety of models and compare against
state-of-the-art polyhedral meshing methods based on clipped Voronoi cells
establishing the clear advantage of VoroCrust output.Comment: 18 pages (including appendix), 18 figures. Version without compressed
images available on https://www.dropbox.com/s/qc6sot1gaujundy/VoroCrust.pdf.
Supplemental materials available on
https://www.dropbox.com/s/6p72h1e2ivw6kj3/VoroCrust_supplemental_materials.pd
A Framework for Dynamic Terrain with Application in Off-road Ground Vehicle Simulations
The dissertation develops a framework for the visualization of dynamic terrains for use in interactive real-time 3D systems. Terrain visualization techniques may be classified as either static or dynamic. Static terrain solutions simulate rigid surface types exclusively; whereas dynamic solutions can also represent non-rigid surfaces. Systems that employ a static terrain approach lack realism due to their rigid nature. Disregarding the accurate representation of terrain surface interaction is rationalized because of the inherent difficulties associated with providing runtime dynamism. Nonetheless, dynamic terrain systems are a more correct solution because they allow the terrain database to be modified at run-time for the purpose of deforming the surface. Many established techniques in terrain visualization rely on invalid assumptions and weak computational models that hinder the use of dynamic terrain. Moreover, many existing techniques do not exploit the capabilities offered by current computer hardware. In this research, we present a component framework for terrain visualization that is useful in research, entertainment, and simulation systems. In addition, we present a novel method for deforming the terrain that can be used in real-time, interactive systems. The development of a component framework unifies disparate works under a single architecture. The high-level nature of the framework makes it flexible and adaptable for developing a variety of systems, independent of the static or dynamic nature of the solution. Currently, there are only a handful of documented deformation techniques and, in particular, none make explicit use of graphics hardware. The approach developed by this research offloads extra work to the graphics processing unit; in an effort to alleviate the overhead associated with deforming the terrain. Off-road ground vehicle simulation is used as an application domain to demonstrate the practical nature of the framework and the deformation technique. In order to realistically simulate terrain surface interactivity with the vehicle, the solution balances visual fidelity and speed. Accurately depicting terrain surface interactivity in off-road ground vehicle simulations improves visual realism; thereby, increasing the significance and worth of the application. Systems in academia, government, and commercial institutes can make use of the research findings to achieve the real-time display of interactive terrain surfaces
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