5,011 research outputs found

    Self-improving Algorithms for Coordinate-wise Maxima

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    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 nn (unknown) independent distributions \cD_1, \cD_2, ..., \cD_n of planar points. An input pointset (p1,p2,...,pn)(p_1, p_2, ..., p_n) is generated by taking an independent sample pip_i 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

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    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

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    We consider random lattice triangulations of n×kn\times k rectangular regions with weight λσ\lambda^{|\sigma|} where λ>0\lambda>0 is a parameter and σ|\sigma| denotes the total edge length of the triangulation. When λ(0,1)\lambda\in(0,1) and kk is fixed, we prove a tight upper bound of order n2n^2 for the mixing time of the edge-flip Glauber dynamics. Combined with the previously known lower bound of order exp(Ω(n2))\exp(\Omega(n^2)) for λ>1\lambda>1 [3], this establishes the existence of a dynamical phase transition for thin rectangles with critical point at λ=1\lambda=1

    Reconstruction and thermal stability of the cubic SiC(001) surfaces

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    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

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    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

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    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

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    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

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    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
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