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On the construction of some capacityapproaching coding schemes
, 2000
"... This thesis proposes two constructive methods of approaching the Shannon limit very closely. Interestingly, these two methods operate in opposite regions, one has a block length of one and the other has a block length approaching infinity. The first approach is based on novel memoryless joint source ..."
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Cited by 82 (2 self)
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This thesis proposes two constructive methods of approaching the Shannon limit very closely. Interestingly, these two methods operate in opposite regions, one has a block length of one and the other has a block length approaching infinity. The first approach is based on novel memoryless joint sourcechannel coding schemes. We first show some examples of sources and channels where no coding is optimal for all values of the signaltonoise ratio (SNR). When the source bandwidth is greater than the channel bandwidth, joint coding schemes based on spacefilling curves and other families of curves are proposed. For uniform sources and modulo channels, our coding scheme based on spacefilling curves operates within 1.1 dB of Shannon’s ratedistortion bound. For Gaussian sources and additive white Gaussian noise (AWGN) channels, we can achieve within 0.9 dB of the ratedistortion bound. The second scheme is based on lowdensity paritycheck (LDPC) codes. We first demonstrate that we can translate threshold values of an LDPC code between channels accurately using a simple mapping. We develop some models for density evolution
On the Metric Properties of Discrete SpaceFilling Curves
, 1996
"... A spacefilling curve is a linear traversal of a discrete finite multidimensional space. In order that this traversal be useful in many applications, the curve should preserve "locality". We quantify "locality" and bound the locality of multidimensional spacefilling curves. Cl ..."
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Cited by 53 (1 self)
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A spacefilling curve is a linear traversal of a discrete finite multidimensional space. In order that this traversal be useful in many applications, the curve should preserve "locality". We quantify "locality" and bound the locality of multidimensional spacefilling curves. Classic Hilbert spacefilling curves come close to achieving optimal locality. EDICS: IP 3.1 Corresponding author: Craig Gotsman Dept. of Computer Science Technion, Haifa 32000 Israel Tel: +9724294336 Fax: +9724294353 Email: gotsman@cs.technion.ac.il # A preliminary version of this work was presented at the IEEE International Conference on Pattern Recognition, Jerusalem, 1994. 1 1
Geometry Caching for RayTracing Displacement Maps
 In Eurographics Rendering Workshop
, 1996
"... We present a technique for rendering displacement mapped geometry in a raytracing renderer. Displacement mapping is an important technique for adding detail to surface geometry in rendering systems. It allows complex geometric variation to be added to simpler geometry, without the cost in geometric ..."
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Cited by 27 (0 self)
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We present a technique for rendering displacement mapped geometry in a raytracing renderer. Displacement mapping is an important technique for adding detail to surface geometry in rendering systems. It allows complex geometric variation to be added to simpler geometry, without the cost in geometric complexity of completely describing the nuances of the geometry at modeling time and with the advantage that the detail can be added adaptively at rendering time. The cost of displacement mapping is geometric complexity. Renderers that provide it must be able to efficiently render scenes that have effectively millions of geometric primitives. Scanline renderers process primitives one at a time, so this complexity doesn't tax them, but traditional raytracing algorithms require random access to the entire scene database, so any part of the scene geometry may need to be available at any point during rendering. If the displaced geometry is fully instantiated in memory, it is straightforward to...
MultiLinearization Data Structure for Image Browsing
 In SPIE { The International Society for Optical Engineering
, 1999
"... Image search has been actively studied in recent years. On the other hands, image browsing has received little attention. Image browsing refers to the process of presenting some forms of overview or summary of the image relationships, thus facilitating a user to navigate across the data set and find ..."
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Cited by 12 (2 self)
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Image search has been actively studied in recent years. On the other hands, image browsing has received little attention. Image browsing refers to the process of presenting some forms of overview or summary of the image relationships, thus facilitating a user to navigate across the data set and find images of interests. In this paper, we present a new data structure built on the multilinearization of image attributes for efficient organization of the data set and fast visual browsing of the images. We describe new techniques for multilinearization based on multiple spacefilling curves and hierarchical clustering techniques. In addition to providing fast navigation, our proposed data structure allows computationally efficient insertion and deletion of images from the data set. We then present a novel image navigator and browser built on duallinearization data structure and intuitive presentation of image relevance and relationships, demonstrate the image navigation process, and repo...
Dynamic Ray Scheduling to Improve Ray Coherence and Bandwidth Utilization
 Proceedings of the IEEE Symposium on Interactive Ray Tracing
, 2007
"... The performance of fullfeatured ray tracers has historically been limited by the hardware’s floating point computational power. However, next generation multithreaded multicore architectures promise to provide sufficient CPU throughput to support real time frame rates. In such systems, limited me ..."
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Cited by 9 (1 self)
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The performance of fullfeatured ray tracers has historically been limited by the hardware’s floating point computational power. However, next generation multithreaded multicore architectures promise to provide sufficient CPU throughput to support real time frame rates. In such systems, limited memory system performance in terms of both onchip cache and DRAMtocache bandwidth is likely to bound overall system performance. This paper presents a novel ray tracing algorithm that both improves cache utilization and reduces DRAMtocache bandwidth usage. The key insight is to view ray traversal as a scheduling problem, which allows our algorithm to match ray traversal computations and intersection computations with available system resources. Using a detailed simulator, we show that our algorithm significantly reduces the amount of data brought into the cache in exchange for the small overhead of maintaining the ray schedule. Moreover, our algorithm creates units of work that are more amenable to parallelization than traditional Whittedstyle ray tracers. Index Terms: I.3.7 [Computer Graphics]: Ray Tracing— 1
Incremental and Hierarchical Hilbert Order Edge Equation Polygon Rasterization
, 2001
"... A rasterization algorithm must efficiently generate pixel fragments from geometric descriptions of primitives. In order to accomplish perpixel shading, shading parameters must also be interpolated across the primitive in a perspectivecorrect manner. If some of these parameters are to be interprete ..."
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Cited by 9 (1 self)
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A rasterization algorithm must efficiently generate pixel fragments from geometric descriptions of primitives. In order to accomplish perpixel shading, shading parameters must also be interpolated across the primitive in a perspectivecorrect manner. If some of these parameters are to be interpreted in later stages of the pipeline directly or indirectly as texture coordinates, then translating spatial and parametric coherence into temporal coherence will improve texture cache performance. Finally, if framebuffer access is also organized around cached blocks, then organizing rasterization so fragments are generated in blocksequential order will maximize framebuffer cache performance. Hilbertorder rasterization accomplishes these goals, and also permits efficient incremental evaluation of edge and interpolation equations.
Volume visualization of multiple alignment of large genomic DNA
 Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data
, 2006
"... Summary. Genomes of hundreds of species have been sequenced to date, and many more are being sequenced. As more and more sequence data sets become available, and as the challenge of comparing these massive “billion basepair DNA sequences” becomes substantial, so does the need for more powerful tools ..."
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Cited by 2 (0 self)
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Summary. Genomes of hundreds of species have been sequenced to date, and many more are being sequenced. As more and more sequence data sets become available, and as the challenge of comparing these massive “billion basepair DNA sequences” becomes substantial, so does the need for more powerful tools supporting the exploration of these data sets. Similarity score data used to compare aligned DNA sequences is inherently onedimensional. Onedimensional (1D) representations of these data sets do not effectively utilize screen real estate. As a result, tools using 1D representations are incapable of providing informatory overview for extremely large data sets. We present a technique to arrange 1D data in 3D space to allow us to apply stateoftheart interactive volume visualization techniques for data exploration. We demonstrate our technique using multimillionsbasepairlong aligned DNA sequence data and compare it with traditional 1D line plots. The results show that our technique is superior in providing an overview of entire data sets. Our technique, coupled with 1D line plots, results in effective multiresolution visualization of very large aligned sequence data sets.
Recursive tilings and spacefilling curves with little fragmentation
 Journal of Computational Geometry
, 2011
"... This paper defines the Arrwwid number of a recursive tiling (or spacefilling curve) as the smallest number a such that any ball Q can be covered by a tiles (or curve sections) with total volume O(volume(Q)). Recursive tilings and spacefilling curves with low Arrwwid numbers can be applied to optim ..."
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This paper defines the Arrwwid number of a recursive tiling (or spacefilling curve) as the smallest number a such that any ball Q can be covered by a tiles (or curve sections) with total volume O(volume(Q)). Recursive tilings and spacefilling curves with low Arrwwid numbers can be applied to optimise disk, memory or server access patterns when processing sets of points in Rd. This paper presents recursive tilings and spacefilling curves with optimal Arrwwid numbers. For d ≥ 3, we see that regular cube tilings and spacefilling curves cannot have optimal Arrwwid number, and we see how to construct alternatives with better Arrwwid numbers.
Dynamic loadbalancing in a lightweight adaptive parallel multigrid PDE solver.
"... A parallel version of an adaptive multigrid solver for partial differential equations is considered. The main emphasis is put on the load balancing algorithm to distribute the adaptive grids at runtime. The background and some applications of spacefilling curves are discussed, which are later on us ..."
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A parallel version of an adaptive multigrid solver for partial differential equations is considered. The main emphasis is put on the load balancing algorithm to distribute the adaptive grids at runtime. The background and some applications of spacefilling curves are discussed, which are later on used as the basic principle of the loadbalancing heuristic. A tight integration of spacefilling curves as a memory addressing scheme into the numerical algorithm is proposed. Some experiments on a cluster of PCs demonstrates the parallel efficiency and scalability of the approach. 1 An adaptive multigrid solver Our goal is to solve a partial differential equation as fast as possible. We consider a multigrid solver, adaptive grid refinement and their efficient parallelization. We have to develop a parallel multigrid code that is almost identical to the sequential implementation. The computational workload has to be distributed into similar sized partitions and, at the same time, the communic...
Abstract Volume Visualization of Multiple Alignment of Genomic DNA
"... Genomes of hundreds of species have been sequenced to date and many more are being sequenced. As more and more sequence data sets become available, and as the challenge of comparing these massive “billion basepair DNA sequences ” becomes substantial, so does the need for more powerful tools supporti ..."
Abstract
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Genomes of hundreds of species have been sequenced to date and many more are being sequenced. As more and more sequence data sets become available, and as the challenge of comparing these massive “billion basepair DNA sequences ” becomes substantial, so does the need for more powerful tools supporting the exploration of these data sets. Similarity score data used to compare aligned DNA sequences is inherently onedimensional. Onedimensional (1D) representations of these data sets do not effectively utilize screen real estate. We present a technique to arrange 1D data in 3D space to allow us to apply stateoftheart interactive volume visualization techniques for data exploration. We provide results for aligned DNA sequence data and compare it with traditional 1D line plots. Our technique, coupled with 1D line plots, results in effective multiresolution visualization of very large aligned sequence data sets.