5,011 research outputs found
Self-improving Algorithms for Coordinate-wise Maxima
Computing the coordinate-wise maxima of a planar point set is a classic and
well-studied problem in computational geometry. We give an algorithm for this
problem in the \emph{self-improving setting}. We have (unknown) independent
distributions \cD_1, \cD_2, ..., \cD_n of planar points. An input pointset
is generated by taking an independent sample from
each \cD_i, so the input distribution \cD is the product \prod_i \cD_i. A
self-improving algorithm repeatedly gets input sets from the distribution \cD
(which is \emph{a priori} unknown) and tries to optimize its running time for
\cD. Our algorithm uses the first few inputs to learn salient features of the
distribution, and then becomes an optimal algorithm for distribution \cD. Let
\OPT_\cD denote the expected depth of an \emph{optimal} linear comparison
tree computing the maxima for distribution \cD. Our algorithm eventually has
an expected running time of O(\text{OPT}_\cD + n), even though it did not
know \cD to begin with.
Our result requires new tools to understand linear comparison trees for
computing maxima. We show how to convert general linear comparison trees to
very restricted versions, which can then be related to the running time of our
algorithm. An interesting feature of our algorithm is an interleaved search,
where the algorithm tries to determine the likeliest point to be maximal with
minimal computation. This allows the running time to be truly optimal for the
distribution \cD.Comment: To appear in Symposium of Computational Geometry 2012 (17 pages, 2
figures
Dynamic Graphs on the GPU
We present a fast dynamic graph data structure for the GPU. Our dynamic graph structure uses one hash table per vertex to store adjacency lists and achieves 3.4–14.8x faster insertion rates over the state of the art across a diverse set of large datasets, as well as deletion speedups up to 7.8x. The data structure supports queries and dynamic updates through both edge and vertex insertion and deletion. In addition, we define a comprehensive evaluation strategy based on operations, workloads, and applications that we believe better characterize and evaluate dynamic graph data structures
Dynamics of Lattice Triangulations on Thin Rectangles
We consider random lattice triangulations of rectangular regions
with weight where is a parameter and
denotes the total edge length of the triangulation. When
and is fixed, we prove a tight upper bound of order
for the mixing time of the edge-flip Glauber dynamics. Combined with the
previously known lower bound of order for [3],
this establishes the existence of a dynamical phase transition for thin
rectangles with critical point at
Reconstruction and thermal stability of the cubic SiC(001) surfaces
The (001) surfaces of cubic SiC were investigated with ab-initio molecular
dynamics simulations. We show that C-terminated surfaces can have different
c(2x2) and p(2x1) reconstructions, depending on preparation conditions and
thermal treatment, and we suggest experimental probes to identify the various
reconstructed geometries. Furthermore we show that Si-terminated surfaces
exhibit a p(2x1) reconstruction at T=0, whereas above room temperature they
oscillate between a dimer row and an ideal geometry below 500 K, and sample
several patterns including a c(4x2) above 500 K.Comment: 12 pages, RevTeX, figures 1 and 2 available in gif form at
http://irrmawww.epfl.ch/fg/sic/fig1.gif and
http://irrmawww.epfl.ch/fg/sic/fig2.gi
Tracking of secondary and temporary objects in structural concrete work
Previous research has shown that “Scan-vs-BIM ” object recognition systems, that fuse 3D point clouds from Terrestrial Laser Scanning (TLS) or digital photogrammetry with 4D project BIM, provide valuable information for tracking structural works. However, until now, the potential of these systems has been demonstrated for tracking progress of permanent structures only; no work has been reported yet on tracking secondary or temporary structures. For structural concrete work, temporary structures include formwork, scaffolding and shoring, while secondary components include rebar. Together, they constitute most of the earned value in concrete work. The impact of tracking such elements would thus be added veracity and detail to earned value calculations, and subsequently better project control and performance. This paper presents three different techniques for recognizing concrete construction secondary and temporary objects in TLS point clouds. Two of the techniques are tested using real-life data collected from a reinforced concrete building construction site. The preliminary experimental results show that it is feasible to recognize secondary and temporary objects in TLS point clouds with good accuracy; but it is envisaged that superior results could be achieved by using additional cues such colour and 3D edge information
Algorithms and Data Structures for Multi-Adaptive Time-Stepping
Multi-adaptive Galerkin methods are extensions of the standard continuous and
discontinuous Galerkin methods for the numerical solution of initial value
problems for ordinary or partial differential equations. In particular, the
multi-adaptive methods allow individual and adaptive time steps to be used for
different components or in different regions of space. We present algorithms
for efficient multi-adaptive time-stepping, including the recursive
construction of time slabs and adaptive time step selection. We also present
data structures for efficient storage and interpolation of the multi-adaptive
solution. The efficiency of the proposed algorithms and data structures is
demonstrated for a series of benchmark problems.Comment: ACM Transactions on Mathematical Software 35(3), 24 pages (2008
On finding widest empty curved corridors
Open archive-ElsevierAn α-siphon of width w is the locus of points in the plane that are at the same distance w from a 1-corner polygonal chain C
such that α is the interior angle of C. Given a set P of n points in the plane and a fixed angle α, we want to compute the widest
empty α-siphon that splits P into two non-empty sets.We present an efficient O(n log3 n)-time algorithm for computing the widest
oriented α-siphon through P such that the orientation of a half-line of C is known.We also propose an O(n3 log2 n)-time algorithm
for the widest arbitrarily-oriented version and an (nlog n)-time algorithm for the widest arbitrarily-oriented α-siphon anchored
at a given point
Charging Induced Emission of Neutral Atoms from NaCl Nanocube Corners
Detachment of neutral cations/anions from solid alkali halides can in
principle be provoked by donating/subtracting electrons to the surface of
alkali halide crystals, but generally constitutes a very endothermic process.
However, the amount of energy required for emission is smaller for atoms
located in less favorable positions, such as surface steps and kinks. For a
corner ion in an alkali halide cube the binding is the weakest, so it should be
easier to remove that atom, once it is neutralized. We carried out first
principles density functional calculations and simulations of neutral and
charged NaCl nanocubes, to establish the energetics of extraction of
neutralized corner ions. Following hole donation (electron removal) we find
that detachment of neutral Cl corner atoms will require a limited energy of
about 0.8 eV. Conversely, following the donation of an excess electron to the
cube, a neutral Na atom is extractable from the corner at the lower cost of
about 0.6 eV. Since the cube electron affinity level (close to that a NaCl(100)
surface state, which we also determine) is estimated to lie about 1.8 eV below
vacuum, the overall energy balance upon donation to the nanocube of a zero
energy electron from vacuum will be exothermic. The atomic and electronic
structure of the NaCl(100) surface, and of the nanocube Na and Cl corner
vacancies are obtained and analyzed as a byproduct.Comment: 16 pages, 2 table, 7 figure
- …