1) The document describes an exact algorithm for solving the Capacitated Arc Routing Problem (CARP) using a parallel branch and bound method.
2) The algorithm constructs feasible solutions by duplicating nodes, constructing minimum cost perfect matchings, and prohibiting arcs to satisfy capacity constraints.
3) Computational experiments on instances with up to 15 demand arcs showed that the parallelization across 6 workstations reduced computing time and solved larger problems compared to a single workstation approach.
An Analytical Expression for Service Curves of Fading ChannelsGiacomo Verticale
In this paper, we develop a method for analyzing time-varying wireless channels in the context of the modern theory of the stochastic network calculus. In particular, our technique is applicable to channels that can be modeled as Markov chains, which is the case of channels subject to Rayleigh fading. Our approach relies on theoretical results on the convergence time of reversible Markov processes and is applicable to chains with an arbitrary number of states. We provide two expressions for the delay tail distribution of traffic transmitted over a fading channel fed by a Markov source. The first expression is tighter and only requires a simple numerical minimization, the second expression is looser, but is in closed form.
A Closed-Form Expression for Queuing Delay in Rayleigh Fading Channels Using ...Giacomo Verticale
This document is a research paper that uses stochastic network calculus to model a wireless channel subject to Rayleigh fading and obtain an approximate closed-form expression for the probability tail of queuing delay. The paper presents the Markovian model of the Rayleigh fading channel, discusses the spectral gap in Markov chains and stochastic network calculus. It then derives the service envelope of the fading channel and compares the queuing delay expression to simulation results, finding a good match between the analysis and simulations. The conclusion is that stochastic network calculus can be used to successfully study wireless channels.
Evidence Of Bimodal Crystallite Size Distribution In Microcrystalline Silico...Sanjay Ram
It is known that there is a bimodal size distribution in microcrystalline silicon. How can the deconvolution of the Raman spectra be done with incorporation of a bimodal CSD to obtain more accurate and physical picture of the microstructure in this material?
Programming with NV_path_rendering: An Annex to the SIGGRAPH Asia 2012 paper...Mark Kilgard
This document provides an overview of the programming interface for NV path rendering, an OpenGL extension for accelerating vector graphics on GPUs. It describes the supported path commands, which are designed to match all major path standards. Paths can be specified explicitly from commands and coordinates, from path strings using grammars like SVG or PostScript, or by generating paths from font glyphs. Additional functions allow copying, interpolating, weighting, or transforming existing path objects.
CSBP: A Fast Circuit Similarity-Based Placement for FPGA Incremental Design a...Xiaoyu Shi
The document presents a circuit similarity-based placement (CSBP) algorithm for FPGA incremental design and design space exploration. CSBP uses an iterative circuit similarity algorithm to compute similarity scores between original and modified circuits. It initializes placement by finding node correspondences based on similarity scores. A low-temperature simulated annealing further refines the results. Experimental results on real circuits show CSBP can successfully find internal node correspondence and achieve better wirelength, delay, and runtime compared to traditional placement tools. The algorithm supports constraints like support and level constraints to enhance performance.
An Analytical Expression for Service Curves of Fading ChannelsGiacomo Verticale
In this paper, we develop a method for analyzing time-varying wireless channels in the context of the modern theory of the stochastic network calculus. In particular, our technique is applicable to channels that can be modeled as Markov chains, which is the case of channels subject to Rayleigh fading. Our approach relies on theoretical results on the convergence time of reversible Markov processes and is applicable to chains with an arbitrary number of states. We provide two expressions for the delay tail distribution of traffic transmitted over a fading channel fed by a Markov source. The first expression is tighter and only requires a simple numerical minimization, the second expression is looser, but is in closed form.
A Closed-Form Expression for Queuing Delay in Rayleigh Fading Channels Using ...Giacomo Verticale
This document is a research paper that uses stochastic network calculus to model a wireless channel subject to Rayleigh fading and obtain an approximate closed-form expression for the probability tail of queuing delay. The paper presents the Markovian model of the Rayleigh fading channel, discusses the spectral gap in Markov chains and stochastic network calculus. It then derives the service envelope of the fading channel and compares the queuing delay expression to simulation results, finding a good match between the analysis and simulations. The conclusion is that stochastic network calculus can be used to successfully study wireless channels.
Evidence Of Bimodal Crystallite Size Distribution In Microcrystalline Silico...Sanjay Ram
It is known that there is a bimodal size distribution in microcrystalline silicon. How can the deconvolution of the Raman spectra be done with incorporation of a bimodal CSD to obtain more accurate and physical picture of the microstructure in this material?
Programming with NV_path_rendering: An Annex to the SIGGRAPH Asia 2012 paper...Mark Kilgard
This document provides an overview of the programming interface for NV path rendering, an OpenGL extension for accelerating vector graphics on GPUs. It describes the supported path commands, which are designed to match all major path standards. Paths can be specified explicitly from commands and coordinates, from path strings using grammars like SVG or PostScript, or by generating paths from font glyphs. Additional functions allow copying, interpolating, weighting, or transforming existing path objects.
CSBP: A Fast Circuit Similarity-Based Placement for FPGA Incremental Design a...Xiaoyu Shi
The document presents a circuit similarity-based placement (CSBP) algorithm for FPGA incremental design and design space exploration. CSBP uses an iterative circuit similarity algorithm to compute similarity scores between original and modified circuits. It initializes placement by finding node correspondences based on similarity scores. A low-temperature simulated annealing further refines the results. Experimental results on real circuits show CSBP can successfully find internal node correspondence and achieve better wirelength, delay, and runtime compared to traditional placement tools. The algorithm supports constraints like support and level constraints to enhance performance.
Tall-and-skinny QR factorizations in MapReduce architecturesDavid Gleich
This document describes using MapReduce to perform a tall-and-skinny QR factorization. It discusses dividing the input matrix into blocks and using mappers to perform QR on each block. The reducers then take the R factors from each block and perform a second stage QR factorization. This allows computing the QR factorization in MapReduce without excessive communication. The document also discusses ways to recover the full Q factor and ensure numerical stability, such as using iterative refinement.
This document chapter discusses manipulator kinematics. It covers forward kinematics, which is determining the end effector position from joint angles. Inverse kinematics is determining the joint angles required for a desired end effector position. The manipulator Jacobian relates joint velocities to end effector velocities. Redundant manipulators have more degrees of freedom than required to perform a task. The chapter provides the procedure for determining the forward kinematics, including using the product of exponentials formula. An example of calculating forward kinematics for a SCARA manipulator is also presented.
This document presents a methodology for mapping multidimensional transforms onto reconfigurable architectures like FPGAs. The methodology uses tensor product decompositions and permutation matrices to express transforms recursively in terms of lower-order blocks. This allows large transforms to be computed by combining many parallel, smaller transform blocks. Specific examples are given for mapping one-dimensional linear convolution and discrete cosine transforms. The overall goal is to provide a unified framework and design process for implementing multidimensional transforms in a modular, parallel architecture.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This document summarizes a lecture on vector graphics and path rendering. It discusses topics like Bézier curves, vector graphic standards, the differences between 3D rendering and path rendering, filling and stroking paths, offset curves for stroking, and challenges with path rendering like sharp turns and overlapping control points. Hard cases are shown where different path rendering implementations produce differing results. Rasterization rules and avoiding conflation artifacts are also covered.
Profiler Zoo introduces several techniques for improving code profiling, such as visualizing test coverage, identifying redundant computation, and using message counting as a proxy for execution time. It presents blueprints for profiling code structure, behavior, and performance bottlenecks. The tool aims to provide more intuitive representations of code profiling compared to traditional approaches.
Dynamic Texture Coding using Modified Haar Wavelet with CUDAIJERA Editor
Texture is an image having repetition of patterns. There are two types, static and dynamic texture. Static texture is an image having repetitions of patterns in the spatial domain. Dynamic texture is number of frames having repetitions in spatial and temporal domain. This paper introduces a novel method for dynamic texture coding to achieve higher compression ratio of dynamic texture using 2D-modified Haar wavelet transform. The dynamic texture video contains high redundant parts in spatial and temporal domain. Redundant parts can be removed to achieve high compression ratios with better visual quality. The modified Haar wavelet is used to exploit spatial and temporal correlations amongst the pixels. The YCbCr color model is used to exploit chromatic components as HVS is less sensitive to chrominance. To decrease the time complexity of algorithm parallel programming is done using CUDA (Compute Unified Device Architecture). GPU contains the number of cores as compared to CPU, which is utilized to reduce the time complexity of algorithms.
This document summarizes a lecture on rate-distortion optimization in video coding. It discusses various rate-distortion optimization problems including operational rate-distortion theory, joint source-channel coding optimization, storage constraint allocation, delay-constrained allocation, buffer-constrained allocation, and the multi-user problem. It also covers convex optimization techniques like the Lagrangian method that can help solve some of these optimization problems.
NV_path_rendering is an OpenGL extension for CUDA-capable NVIDIA GPUs for performing resolution-independent 2D rendering. Standards such as Scalable Vector Graphics (SVG), PostScript, PDF, Adobe Flash, and TrueType fonts rely on path rendering. With NV_path_rendering, this important class of rendering is accelerated by the GPU in a way that co-exists with conventional 3D rendering.
For more information see:
http://developer.nvidia.com/nv-path-rendering
This summarizes a fast re-route method to find an alternate path after a link failure, before the interior gateway protocol has reconverged. The method selects the next hop among a source node's neighbors based on which has the lowest number of visits (multiplicity) and shortest estimated distance to the destination. It is proven to always find an alternate path if one exists. The method improves over loop-free alternate approaches by not requiring tunnels. It can find paths for simple cases like a square topology where LFA fails.
This document discusses the optimal design of CMOS operational amplifiers (op-amps) using geometric programming. It begins by introducing CMOS op-amps and the goal of sizing transistors to meet performance specifications while minimizing area and power. The problem is formulated as a convex optimization that can be solved efficiently. Numerical experiments show the approach finds the globally optimal solution. The accuracy of performance predictions is verified against circuit simulations. Finally, the document provides background on geometric programming and defines the standard form of a geometric program that is used to solve the CMOS op-amp sizing problem.
The document contains 30 multiple choice questions related to mathematics. The questions cover a range of topics including algebra, geometry, trigonometry, calculus, and probability. Each question is followed by 4 possible answer choices.
This document presents a new approach to analyzing the robustness of the relative gain array (RGA) for uncertain systems. It derives bounds on the RGA elements for a 2x2 uncertain system and provides sufficient conditions to determine if the plant remains non-singular over the uncertainty set. An example is provided to illustrate the bounds on the magnitude and phase of the RGA in the frequency domain for an uncertain system. The analysis of the RGA's robustness to uncertainties can help assess decisions made based on the nominal plant model.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
The document presents a modal analysis of a new type of non-conventional optical waveguide with a trapezoidal cross-section and metallic cladding. It derives the characteristic equations using Goell's point matching method under the weak-guidance approximation. It obtains the dispersion curves for different cases of the proposed trapezoidal waveguide and compares them to those of a standard square waveguide with metallic cladding. The analysis shows that distorting a square waveguide into a trapezoidal shape with metallic cladding shifts the lowest cut-off value to a higher value and increases the number of modes.
This document summarizes a study of modified noise-shaper architectures for oversampled sigma-delta digital-to-analog converters (ΣΔDACs). Two hybrid architectures, A1 and A2, are investigated to trade off noise-shaper and digital-to-analog converter (DAC) complexity while maintaining signal-to-noise ratio (SNR). Simulation results show that architecture A1 achieves fairly good SNR by reducing the number of bits to the noise shaper, while architecture A2 further reduces DAC complexity at the cost of doubling the number of DACs. The number of required DAC unit elements is computed and compared for different architectures and parameter values, illustrating the complexity tradeoffs between noise shaping
[Harvard CS264] 13 - The R-Stream High-Level Program Transformation Tool / Pr...npinto
The document describes the R-Stream high-level program transformation tool. It provides an overview of R-Stream, walks through the compilation process, and discusses performance results. R-Stream uses the polyhedral model to perform program transformations like loop transformations, fusion, distribution and tiling to optimize for parallelism and locality. It models the target machine and uses this to inform the mapping of operations to resources like GPUs.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
This document presents a transit time model for short gate length ion-implanted GaAs MESFETs. It develops a 2D analytical model to calculate the potential distribution and electric field in the channel region. Based on this, it derives an expression for transit time by considering the carrier velocity and saturation effects. It also presents an equation for drain current as a function of transit time, doping profile, and other device parameters. Simulation results using MATLAB are shown for Id-Vd characteristics and transit time for different device geometry and material parameters. The model aims to better understand the underlying device physics of optically controlled GaAs MESFETs.
An O(log^2 k)-approximation algorithm for k-vertex connected spanning subgraphlbundit
The algorithm finds a low-cost survivable network using a technique called covering fragments. It starts with connectivity of 1 and incrementally increases the connectivity by covering fragments. The algorithm works as follows:
1. It identifies small fragments called cores and the halo-sets containing each core.
2. It adds edges to cover all fragments in the halo-set of each core. This decreases the number of cores by at least half in each iteration.
3. The algorithm repeats until no cores remain, indicating the network is survivable.
The analysis shows that each iteration decreases the number of cores by half while paying cost of at most 4 times the optimal. Therefore, the overall approximation ratio is O(
Mesh Generation and Topological Data AnalysisDon Sheehy
The document discusses mesh generation as a preprocessing step for topological data analysis (TDA). It describes how mesh generation can be used to decompose a domain into simple elements to approximate functions and compute persistence diagrams. Specifically, generating a quality Voronoi mesh allows the Voronoi filtration to approximate the sublevel filtration of the function and provide a good approximation of the persistence diagram. While meshing may not seem like an obvious approach for TDA, the document argues it can provide the necessary geometric and topological guarantees to make it a valid preprocessing step.
Tall-and-skinny QR factorizations in MapReduce architecturesDavid Gleich
This document describes using MapReduce to perform a tall-and-skinny QR factorization. It discusses dividing the input matrix into blocks and using mappers to perform QR on each block. The reducers then take the R factors from each block and perform a second stage QR factorization. This allows computing the QR factorization in MapReduce without excessive communication. The document also discusses ways to recover the full Q factor and ensure numerical stability, such as using iterative refinement.
This document chapter discusses manipulator kinematics. It covers forward kinematics, which is determining the end effector position from joint angles. Inverse kinematics is determining the joint angles required for a desired end effector position. The manipulator Jacobian relates joint velocities to end effector velocities. Redundant manipulators have more degrees of freedom than required to perform a task. The chapter provides the procedure for determining the forward kinematics, including using the product of exponentials formula. An example of calculating forward kinematics for a SCARA manipulator is also presented.
This document presents a methodology for mapping multidimensional transforms onto reconfigurable architectures like FPGAs. The methodology uses tensor product decompositions and permutation matrices to express transforms recursively in terms of lower-order blocks. This allows large transforms to be computed by combining many parallel, smaller transform blocks. Specific examples are given for mapping one-dimensional linear convolution and discrete cosine transforms. The overall goal is to provide a unified framework and design process for implementing multidimensional transforms in a modular, parallel architecture.
IOSR Journal of Electronics and Communication Engineering(IOSR-JECE) is an open access international journal that provides rapid publication (within a month) of articles in all areas of electronics and communication engineering and its applications. The journal welcomes publications of high quality papers on theoretical developments and practical applications in electronics and communication engineering. Original research papers, state-of-the-art reviews, and high quality technical notes are invited for publications.
This document summarizes a lecture on vector graphics and path rendering. It discusses topics like Bézier curves, vector graphic standards, the differences between 3D rendering and path rendering, filling and stroking paths, offset curves for stroking, and challenges with path rendering like sharp turns and overlapping control points. Hard cases are shown where different path rendering implementations produce differing results. Rasterization rules and avoiding conflation artifacts are also covered.
Profiler Zoo introduces several techniques for improving code profiling, such as visualizing test coverage, identifying redundant computation, and using message counting as a proxy for execution time. It presents blueprints for profiling code structure, behavior, and performance bottlenecks. The tool aims to provide more intuitive representations of code profiling compared to traditional approaches.
Dynamic Texture Coding using Modified Haar Wavelet with CUDAIJERA Editor
Texture is an image having repetition of patterns. There are two types, static and dynamic texture. Static texture is an image having repetitions of patterns in the spatial domain. Dynamic texture is number of frames having repetitions in spatial and temporal domain. This paper introduces a novel method for dynamic texture coding to achieve higher compression ratio of dynamic texture using 2D-modified Haar wavelet transform. The dynamic texture video contains high redundant parts in spatial and temporal domain. Redundant parts can be removed to achieve high compression ratios with better visual quality. The modified Haar wavelet is used to exploit spatial and temporal correlations amongst the pixels. The YCbCr color model is used to exploit chromatic components as HVS is less sensitive to chrominance. To decrease the time complexity of algorithm parallel programming is done using CUDA (Compute Unified Device Architecture). GPU contains the number of cores as compared to CPU, which is utilized to reduce the time complexity of algorithms.
This document summarizes a lecture on rate-distortion optimization in video coding. It discusses various rate-distortion optimization problems including operational rate-distortion theory, joint source-channel coding optimization, storage constraint allocation, delay-constrained allocation, buffer-constrained allocation, and the multi-user problem. It also covers convex optimization techniques like the Lagrangian method that can help solve some of these optimization problems.
NV_path_rendering is an OpenGL extension for CUDA-capable NVIDIA GPUs for performing resolution-independent 2D rendering. Standards such as Scalable Vector Graphics (SVG), PostScript, PDF, Adobe Flash, and TrueType fonts rely on path rendering. With NV_path_rendering, this important class of rendering is accelerated by the GPU in a way that co-exists with conventional 3D rendering.
For more information see:
http://developer.nvidia.com/nv-path-rendering
This summarizes a fast re-route method to find an alternate path after a link failure, before the interior gateway protocol has reconverged. The method selects the next hop among a source node's neighbors based on which has the lowest number of visits (multiplicity) and shortest estimated distance to the destination. It is proven to always find an alternate path if one exists. The method improves over loop-free alternate approaches by not requiring tunnels. It can find paths for simple cases like a square topology where LFA fails.
This document discusses the optimal design of CMOS operational amplifiers (op-amps) using geometric programming. It begins by introducing CMOS op-amps and the goal of sizing transistors to meet performance specifications while minimizing area and power. The problem is formulated as a convex optimization that can be solved efficiently. Numerical experiments show the approach finds the globally optimal solution. The accuracy of performance predictions is verified against circuit simulations. Finally, the document provides background on geometric programming and defines the standard form of a geometric program that is used to solve the CMOS op-amp sizing problem.
The document contains 30 multiple choice questions related to mathematics. The questions cover a range of topics including algebra, geometry, trigonometry, calculus, and probability. Each question is followed by 4 possible answer choices.
This document presents a new approach to analyzing the robustness of the relative gain array (RGA) for uncertain systems. It derives bounds on the RGA elements for a 2x2 uncertain system and provides sufficient conditions to determine if the plant remains non-singular over the uncertainty set. An example is provided to illustrate the bounds on the magnitude and phase of the RGA in the frequency domain for an uncertain system. The analysis of the RGA's robustness to uncertainties can help assess decisions made based on the nominal plant model.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
The document presents a modal analysis of a new type of non-conventional optical waveguide with a trapezoidal cross-section and metallic cladding. It derives the characteristic equations using Goell's point matching method under the weak-guidance approximation. It obtains the dispersion curves for different cases of the proposed trapezoidal waveguide and compares them to those of a standard square waveguide with metallic cladding. The analysis shows that distorting a square waveguide into a trapezoidal shape with metallic cladding shifts the lowest cut-off value to a higher value and increases the number of modes.
This document summarizes a study of modified noise-shaper architectures for oversampled sigma-delta digital-to-analog converters (ΣΔDACs). Two hybrid architectures, A1 and A2, are investigated to trade off noise-shaper and digital-to-analog converter (DAC) complexity while maintaining signal-to-noise ratio (SNR). Simulation results show that architecture A1 achieves fairly good SNR by reducing the number of bits to the noise shaper, while architecture A2 further reduces DAC complexity at the cost of doubling the number of DACs. The number of required DAC unit elements is computed and compared for different architectures and parameter values, illustrating the complexity tradeoffs between noise shaping
[Harvard CS264] 13 - The R-Stream High-Level Program Transformation Tool / Pr...npinto
The document describes the R-Stream high-level program transformation tool. It provides an overview of R-Stream, walks through the compilation process, and discusses performance results. R-Stream uses the polyhedral model to perform program transformations like loop transformations, fusion, distribution and tiling to optimize for parallelism and locality. It models the target machine and uses this to inform the mapping of operations to resources like GPUs.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
This document presents a transit time model for short gate length ion-implanted GaAs MESFETs. It develops a 2D analytical model to calculate the potential distribution and electric field in the channel region. Based on this, it derives an expression for transit time by considering the carrier velocity and saturation effects. It also presents an equation for drain current as a function of transit time, doping profile, and other device parameters. Simulation results using MATLAB are shown for Id-Vd characteristics and transit time for different device geometry and material parameters. The model aims to better understand the underlying device physics of optically controlled GaAs MESFETs.
An O(log^2 k)-approximation algorithm for k-vertex connected spanning subgraphlbundit
The algorithm finds a low-cost survivable network using a technique called covering fragments. It starts with connectivity of 1 and incrementally increases the connectivity by covering fragments. The algorithm works as follows:
1. It identifies small fragments called cores and the halo-sets containing each core.
2. It adds edges to cover all fragments in the halo-set of each core. This decreases the number of cores by at least half in each iteration.
3. The algorithm repeats until no cores remain, indicating the network is survivable.
The analysis shows that each iteration decreases the number of cores by half while paying cost of at most 4 times the optimal. Therefore, the overall approximation ratio is O(
Mesh Generation and Topological Data AnalysisDon Sheehy
The document discusses mesh generation as a preprocessing step for topological data analysis (TDA). It describes how mesh generation can be used to decompose a domain into simple elements to approximate functions and compute persistence diagrams. Specifically, generating a quality Voronoi mesh allows the Voronoi filtration to approximate the sublevel filtration of the function and provide a good approximation of the persistence diagram. While meshing may not seem like an obvious approach for TDA, the document argues it can provide the necessary geometric and topological guarantees to make it a valid preprocessing step.
The document provides an overview and outline of the course "Optimization for Machine Learning". Key points:
- The course covers topics like convexity, gradient methods, constrained optimization, proximal algorithms, stochastic gradient descent, and more.
- Mathematical modeling and computational optimization for machine learning are discussed. Optimization algorithms like gradient descent and stochastic gradient descent are important for learning model parameters.
- Convex optimization problems have desirable properties like every local minimum being a global minimum. Gradient descent and related algorithms are guaranteed to converge for convex problems.
- Convex sets and functions are introduced, including characterizations using epigraphs and subgradients. Convex functions have useful properties like continuity and satisfying Jensen's inequality.
Shor's discrete logarithm quantum algorithm for elliptic curvesXequeMateShannon
This document summarizes John Proos and Christof Zalka's research on implementing Shor's quantum algorithm for solving the discrete logarithm problem over elliptic curves. It shows that for elliptic curve cryptography, a quantum computer could solve problems beyond the capabilities of classical computers using fewer qubits than for integer factorization. Specifically, a 160-bit elliptic curve key could be broken using around 1000 qubits, compared to 2000 qubits needed to factor a 1024-bit RSA modulus. The main technical challenge is implementing the extended Euclidean algorithm to compute multiplicative inverses modulo a prime p.
Sorting and Routing on Hypercubes and Hypercubic ArchitecturesCTOGreenITHub
This document provides an overview of Part IV of the course material which covers low-diameter architectures like hypercubes. It includes 4 slides:
Slide 1 introduces the topics to be covered in Part IV including hypercubes, their algorithms, sorting and routing on hypercubes, other hypercubic architectures, and other network topologies.
Slide 2 provides background information on the presentation including its purpose to support a textbook, author, revisions, and topics to be covered in chapters 13-16.
Slide 3 lists the chapter topics for Chapter 13 including definitions and properties of hypercubes, embeddings and their usefulness, embedding of arrays and trees, and some simple algorithms.
Slide 4 introduces Chapter 13 and lists
Support Vector Machines in MapReduce presented an overview of support vector machines (SVMs) and how to implement them in a MapReduce framework to handle large datasets. The document discussed the theory behind basic linear SVMs and generalized multi-classification SVMs. It explained how to parallelize SVM training using stochastic gradient descent and randomly distributing samples across mappers and reducers. The document also addressed handling non-linear SVMs using kernel methods and approximations that allow SVMs to be treated as a linear problem in MapReduce. Finally, examples were given of large companies using SVMs trained on MapReduce to perform customer segmentation and improve inventory value.
Reproducible Linear Algebra from Application to ArchitectureJason Riedy
All computing must be parallel to take advantage of modern systems like multicore processors, GPUs, and distributed systems. Results that are not bit-wise reproducible introduce doubt on many levels. Sometimes that is appropriate. Reproducibility limitations occur because underlying libraries do not specify their reproducibility requirements. New advances in interfaces, algorithms, and architectures allow selecting among those requirements in the future. This talk covers many of the upcoming options and their trade-offs.
The SpeedIT provides a partial acceleration of sparse linear solvers. Acceleration is achieved with a single reasonably priced NVIDIA Graphics Processing Unit (GPU) that supporst CUDA and proprietary advanced optimisation techniques.
Check also SpeedIT FLOW, our RANS single phase flow solver that runs fully on GPU: vratis.com/blog
This document describes a fast single-pass k-means clustering algorithm. It begins with an overview and rationale for using k-means clustering to enable fast search through large datasets. It then covers the theory behind clusterable data and k-means failure modes. The document outlines ball k-means and surrogate clustering algorithms. It discusses how to implement fast vector search methods like locality sensitive hashing. The document presents results on synthetic datasets and discusses applications like customer segmentation for a company with 100 million customers.
The document discusses kernelization, which is a polynomial-time transformation that maps an instance of a parameterized problem to an equivalent instance whose size is bounded by a function of the parameter k. If a problem admits a kernelization algorithm, then it is fixed-parameter tractable. The document introduces kernelization and provides definitions. It also notes that every fixed-parameter tractable problem has a kernelization algorithm.
[Harvard CS264] 12 - Irregular Parallelism on the GPU: Algorithms and Data St...npinto
The document discusses irregular parallelism on GPUs and presents several algorithms and data structures for handling irregular workloads efficiently in parallel. It covers sparse matrix-vector multiplication using different sparse matrix formats. It also discusses compositing of fragments in parallel and presents a nested data parallel approach. The document describes challenges with parallel hashing and presents a two-level hashing scheme. It analyzes parallel task queues and work stealing techniques for load balancing irregular work. Throughout, it focuses on managing communication in addition to computation for optimal parallel performance.
Hybrid Evolutionary Algorithms on Minimum Vertex Cover for Random GraphsMartin Pelikan
This work analyzes the hierarchical Bayesian optimization algorithm (hBOA) on minimum vertex cover for standard classes of random graphs and transformed SAT instances. The performance of hBOA is compared with that of the branch-and-bound problem solver (BB), the simple genetic algorithm (GA) and the parallel simulated annealing (PSA). The results indicate that BB is significantly outperformed by all the other tested methods, which is expected as BB is a complete search algorithm and minimum vertex cover is an NP-complete problem. The best performance is achieved by hBOA; nonetheless, the performance differences between hBOA and other evolutionary algorithms are relatively small, indicating that mutation-based search and recombination-based search lead to similar performance on the tested classes of minimum vertex cover problems.
Incremental pattern matching in the VIATRA2 model transformation systemIstvan Rath
Incremental pattern matching allows model transformations to update target models incrementally based on changes to the source model. The VIATRA model transformation system implements incremental pattern matching using a RETE network to efficiently retrieve matching sets as models change. Benchmark results show near-linear performance for sparse models and constant execution time for certain patterns. Future work includes improving construction algorithms and enabling event-driven live transformations.
Wrapper induction construct wrappers automatically to extract information f...George Ang
Wrapper induction is a technique to automatically generate wrappers to extract information from web sources. It involves learning extraction rules from labeled examples to construct a wrapper as a finite state machine or set of delimiters. Two main wrapper induction systems are WIEN, which defines wrapper classes including LR, and STALKER, which uses a more expressive model with extraction rules and landmarks to handle structure hierarchically. Remaining challenges include selecting informative examples, generating label pages automatically, and developing more expressive models.
All Pair Shortest Path Algorithm – Parallel Implementation and AnalysisInderjeet Singh
This project report discusses the parallel implementation of the all pair shortest path algorithm using MPI and OpenMP. The algorithm was implemented by decomposing the adjacency matrix row-wise across processes. Results show that the parallel algorithm achieves speedup over the sequential version, especially for large graph sizes. The MPI implementation performed better than the OpenMP version. Graphs in the report compare execution time, speedup, and efficiency for different problem sizes and numbers of processes/threads.
(Paper) Efficient Evaluation Methods of Elementary Functions Suitable for SIM...Naoki Shibata
Naoki Shibata : Efficient Evaluation Methods of Elementary Functions Suitable for SIMD Computation, Journal of Computer Science on Research and Development, Proceedings of the International Supercomputing Conference ISC10., Volume 25, Numbers 1-2, pp. 25-32, DOI:10.1007/s00450-010-0108-2 (May. 2010).
http://ito-lab.naist.jp/~n-sibata/pdfs/isc10simd.pdf
http://freecode.com/projects/sleef
Data-parallel architectures like SIMD (Single Instruction Multiple Data) or SIMT (Single Instruction Multiple Thread) have been adopted in many recent CPU and GPU architectures. Although some SIMD and SIMT instruction sets include double-precision arithmetic and bitwise operations, there are no instructions dedicated to evaluating elementary functions like trigonometric functions in double precision. Thus, these functions have to be evaluated one by one using an FPU or using a software library. However, traditional algorithms for evaluating these elementary functions involve heavy use of conditional branches and/or table look-ups, which are not suitable for SIMD computation. In this paper, efficient methods are proposed for evaluating the sine, cosine, arc tangent, exponential and logarithmic functions in double precision without table look-ups, scattering from, or gathering into SIMD registers, or conditional branches. We implemented these methods using the Intel SSE2 instruction set to evaluate their accuracy and speed. The results showed that the average error was less than 0.67 ulp, and the maximum error was 6 ulps. The computation speed was faster than the FPUs on Intel Core 2 and Core i7 processors.
ICIAM 2019: Reproducible Linear Algebra from Application to ArchitectureJason Riedy
All computing must be parallel to take advantage of modern systems like multicore processors, GPUs, and distributed systems. Results that are not bit-wise reproducible introduce doubt on many levels. Sometimes that is appropriate. Reproducibility limitations occur because underlying libraries do not specify their reproducibility requirements. New advances in interfaces, algorithms, and architectures allow selecting among those requirements in the future. This talk covers many of the upcoming options and their trade-offs.
PR-297: Training data-efficient image transformers & distillation through att...Jinwon Lee
안녕하세요 TensorFlow Korea 논문 읽기 모임 PR-12의 297번째 리뷰입니다
어느덧 PR-12 시즌 3의 끝까지 논문 3편밖에 남지 않았네요.
시즌 3가 끝나면 바로 시즌 4의 새 멤버 모집이 시작될 예정입니다. 많은 관심과 지원 부탁드립니다~~
(멤버 모집 공지는 Facebook TensorFlow Korea 그룹에 올라올 예정입니다)
오늘 제가 리뷰한 논문은 Facebook의 Training data-efficient image transformers & distillation through attention 입니다.
Google에서 나왔던 ViT논문 이후에 convolution을 전혀 사용하지 않고 오직 attention만을 이용한 computer vision algorithm에 어느때보다 관심이 높아지고 있는데요
이 논문에서 제안한 DeiT 모델은 ViT와 같은 architecture를 사용하면서 ViT가 ImageNet data만으로는 성능이 잘 안나왔던 것에 비해서
Training 방법 개선과 새로운 Knowledge Distillation 방법을 사용하여 mageNet data 만으로 EfficientNet보다 뛰어난 성능을 보여주는 결과를 얻었습니다.
정말 CNN은 이제 서서히 사라지게 되는 것일까요? Attention이 computer vision도 정복하게 될 것인지....
개인적으로는 당분간은 attention 기반의 CV 논문이 쏟아질 거라고 확신하고, 또 여기에서 놀라운 일들이 일어날 수 있을 거라고 생각하고 있습니다
CNN은 10년간 많은 연구를 통해서 발전해왔지만, transformer는 이제 CV에 적용된 지 얼마 안된 시점이라서 더 기대가 크구요,
attention이 inductive bias가 가장 적은 형태의 모델이기 때문에 더 놀라운 이들을 만들 수 있을거라고 생각합니다
얼마 전에 나온 open AI의 DALL-E도 그 대표적인 예라고 할 수 있을 것 같습니다. Transformer의 또하나의 transformation이 궁금하신 분들은 아래 영상을 참고해주세요
영상링크: https://youtu.be/DjEvzeiWBTo
논문링크: https://arxiv.org/abs/2012.12877
This document summarizes two matrix computation algorithms:
1) PageRank, which computes the principal eigenvector of the Google matrix using an inner-outer iteration instead of the power method. This improves speed on large graphs.
2) Network alignment, which aligns two networks by solving an integer quadratic program to match nodes based on edge connections. Results show near-optimal alignment in minutes on large networks.
The talk provides context on these algorithms, theoretical background, and empirical results demonstrating faster performance on large real-world networks compared to alternative approaches.
Data-Intensive Computing for Competent Genetic Algorithms: A Pilot Study us...Xavier Llorà
Data-intensive computing has positioned itself as a valuable programming paradigm to efficiently approach problems requiring processing very large volumes of data. This paper presents a pilot study about how to apply the data-intensive computing paradigm to evolutionary computation algorithms. Two representative cases (selectorecombinative genetic algorithms and estimation of distribution algorithms) are presented, analyzed, and discussed. This study shows that equivalent data-intensive computing evolutionary computation algorithms can be easily developed, providing robust and scalable algorithms for the multicore-computing era. Experimental results show how such algorithms scale with the number of available cores without further modification.
Data-Intensive Computing for Competent Genetic Algorithms: A Pilot Study us...
Shuronr
1. An Exact Algorithm for the
Capacitated Arc Routing Problem using
Parallel Branch and Bound Method
~ An Experimental Verification on the Effect of Parallelization ~
Masaaki Kiuchi (Hirabayashi Lab.)
Department of Management Science,
Faculty of Engineering,
Science University of Tokyo
2. CONTENTS
1: Introduction
2: Capacitated Arc Routing Problem
3: Parallel Tour Construction
Algorithm
– 3-1: Lower Bounding Procedure
– 3-2: Branching Scheme
– 3-3: Constructing a Feasible Solution
4: Computational Experiments
3. 1: Introduction
Classification of Routing Problems
Service activities Service activities
Routing Problem are required on
are required at
Nodes !! Arcs !!
Node Routing Problem Arc Routing Problem
TSP : CPP :
Traveling Salesman Chinese Postman Problem
Problem Demand constraint !
Demand constraint ! RPP :
and
Rural Postman Problem
Capacity constraint !
Capacity constraint !
VRP : CARP :
Vehicle Routing Problem Capacitated Arc Routing Problem
4. 1: Introduction
Background of the Study
Previous Works on the CARP Branch and Bound
Heuristic Algorithms Few relationships between each subproblems!
1964: Clarke and Wright ex. Calculation of a relaxation problem
・・・ Branching operation in a subproblem
1993: Chang Improvement by
Lower Bounding Procedures parallelization!
1981: Golden and Wong Parallel Branch and Bound
・・・
1994: Y.Shinano et al.
1992: Y.Saruwatari et al. ‘‘PUBB: Parallelization Utility
‘‘Node Duplication for Branch and
Lower Bounding Procedure’’ Bound’’
Exact Algorithms In expectation of ...
1992: Y.Saruwatari et al. ・ Reduction of the Computing Time!
‘‘Tour Construction Algorithm’’ ・ Application to Larger Instances!
5. 2: Capacitated Arc Routing Problem
Summary of the Problem
〒
How to deliver ? depot
?
〒 demand
distance= 2 2
capacity ... cost
Graph : G = V , E 1 1
depot : v 0 ∈ V
cost : c( e) ≥0 3 3
demand : q ( e) ≥0 3
capacity : D ≥ max q e
e∈E
6. 2: Capacitated Arc Routing Problem
Formulation of the Problem
CARP : Branch and Bound
K : positive integer,
W 1, W 2 , , WK : K closed walks in G , relaxation
find
Fi : ⊆ E ( Wi ) , problem
( i = 1,2, , K ) .
v 0 ∈ ( Wi ) , ( i = 1,2, , K ) ,
V (1)
K
Fi = E D , Fi ∩ Fj = ∅,
i =1 (2) Continue the calculation
to satisfy
sub.to. (E D
)
= { e ∈E | q ( e) > 0} , the constraint (3).
∑ q( e) ≤ D, ( i = 1,2, , K ) ,
e∈ i
F
(3)
∑ ∑ ( ) c( e) is minimum.
K
i =1 e ∈ Wi
E
(4) feasible solution!!
7. 3: Parallel Tour Construction Algorithm
Summary of Our Parallelization
Branch and Bound A Framework of the
Parallel Branch and Bound
subproblems
Master processor
TCP/IP
Each subproblem can be
solved independently!
feasible solution!! Slave processors
8. 3: Parallel Tour Construction Algorithm
Summary of the Algorithm
The Framework of the PUBB: ・ read instance data
・ construct Node
Parallelization Utility for Branch and Bound
Duplicated Graph
・ construct
Master Process
Modified Graph
Master processor ・ management of the search tree
・ assignment of subproblems
・ Modified Graph
Slave Processes ・ Information about
TCP/IP
・ calculation on prohibited arcs
subproblems
・ branching operations
Slave Buffer Processes ・ construct
・ buffer of each slave Matching Graph
process ・ solve the MCPM
Slave Controller Process ・ branching operation
Slave processors ・ generate
・ management of the
slave processes on a WS subproblems
9. 3-1: Lower Bounding Procedure
What is the Minimum Cost Perfect Matching ?
Definition of Matching
Minimum Cost
If no two arcs in a subset M of E are adjacent, Perfect Matching
then M is called a matching in G=(V,E).
3 3
For example ...
Matching Perfect Matching
3 2
3
5
5 3 + 3 + 3 + 2 = 11
All the nodes in G are
6 endpoints of arcs in M,
5 + 3 + 5 + 6 = 19
and
Not all the nodes in G are All the nodes in G are the sum of weights of
endpoints of arcs in M. endpoints of arcs in M. arcs in M is minimum.
10. 3-1: Lower Bounding Procedure
Node Duplication Lower Bounding Procedure
served arcs: demand arcs Served by exactly one vehicle!
〒 passed arcs: demand arcs Control the total cost of
non-demand arcs routes of some vehicles!
1 1
(2,2) (2,2) Separate all the 2 2H 2
demand arcs!
(1,3) (1,3) 3 3
2 3 4
Duplicate all the
(3,2) nodes in the graph! 2 3 2 4
(3,3) (3,1) 3 1
5 H=
∑ q D=
e 16 / 4 = 4
cost demand
e ∈E 5
demand
11. 3-1: Lower Bounding Procedure
Node Duplicated Graph (perfect graph)
cost: c( e), e ∈E
1
・ demand arcs: ∞
・ arcs in a family: 0
2
(family of depot: ∞
2
)
・ arcs between families:
3
costs of shortest path
3
2 3 4
2
3 1
family 5
12.
13. 3-1: Lower Bounding Procedure
Modified Graph
cost: c( e), e ∈E
1
・ demand arcs: ∞
・ arcs in a family: 0
2
(family of depot: ∞
2
)
・ arcs between families:
3
costs of shortest path
3
If the sum of demands
of two demand arcs:
2 3 4 2+3=5
2
> 4 = D : capacity,
3 1
then reset the costs of non-demand arcs
5
between the two demand arcs ∞ .
14. 3-1: Lower Bounding Procedure
Matching Graph
cost: c( e), e ∈E
1
・ demand arcs: ∞
・ arcs in a family: 0
(family of depot: ∞ )
・ arcs between families:
3
costs of shortest path
3
Remove the two noeds which
are adjacent to demand arcs
2 3 4 from the family of depot
2 and all the arcs which are
3 1 adjacent to the two nodes.
5
15. Minimum Cost Perfect Matching
2 2
Solve the minimum cost perfect matching
problem on the matching graph!
16. 3-1: Lower Bounding Procedure
Matching Graph Minimum Cost Perfect Matching
cost: c( e), e ∈E
1
・ demand arcs: ∞
・ arcs in a family: 0
2
(family of depot: ∞
2
)
・ arcs between families:
3
costs of shortest path
3
Remove the two noeds which
are adjacent to demand arcs
2 3 4 from the family of depot
2 and all the arcs which are
3 1 adjacent to the two nodes.
Solve the minimum cost perfect matching
problem on the matching graph!
5
17. 3-1: Lower Bounding Procedure
Each Delivery Route on the Original Graph (Infeasible!)
1 1 1
(2,2) (2,2) (2,2) (2,2) (2,2) (2,2)
(1,3) (1,3) (1,3) (1,3)
2 3 4 2 3 4 2 3 4
(3,2)
(3,3) (3,1) (3,1)
1 5 2 5 3 5
1 : served arcs
(2,2) (2,2) notice! : passed arcs
(1,3) (1,3) then the route does not satisfy
2 3 4 If the sum of demands on
a route of a vehicle: the capacity constraint!
2+2+1+3=8
The optimal value of a relaxation
4 5 > 4 = D : capacity,
problem = lower bound!
18. 3-2: Branching Scheme
Selection of a Branching Arc
Solve |M| minimum cost perfect
1 matching problems with
each arc in M is prohibited.
2 2
Compare lower bounds
c E D +c M ,
then ...
3 3
find a branching arc in M
which gives the
largest lower bound.
2 3 4
2 Construct two
3 1 subproblems ...
in which the branching in which the branching
arc is contained as a part arc is prohibited as a part
of a path of a vehicle. of a path of a vehicle.
5
19. 3-3: Constructing a Feasible Solution
How to Construct a Feasible Solution ?
Parallel Branch and Bound
1
2 2 contained prohibited
3 3
contained Select a branching arc
contained in each subproblem,
2 3 4
2 and construct a tour of
3 a vehicle to satisfy the
1
capacity constraint.
Prohibited by the
capacity constraint.
feasible solution!!
5
20. 3-3: Constructing a Feasible Solution
Prohibiting Arcs
Calculate the sum of demands
1 on the two demand arcs which
are adjacent to a contained arc
2 2 2 + 2 = 4.
Add one more demand arc
3 3 to a path of a vehicle.
If the sum of demands on
the path of a vehicle:
contained 2+2+1=4+1=5
2 3 4 > 4 = D : capacity,
2
3 1
then prohibit the non-demand arcs
between the path and the demand arc.
5
21. 3-3: Constructing a Feasible Solution
Update the Number of Vehicles
Since the number of vehicles
1 is fixed to H in
each relaxation problem,
2 2
in constructing the
tours of vehicles,
3 3
there may not exist a
solution which satisfies
the capacity constraint.
2 3 4
2
3 The sum of demands on
a route of a vehicle: so, the route does
1 not satisfy the
3+1+2=6
capacity constraint!
> 4 = D : capacity,
5
22. 3-3: Constructing a Feasible Solution
Update the Number of Vehicles
Since the number of vehicles
1 is fixed to H in
each relaxation problem,
2 2
in constructing the
tours of vehicles,
3 3 there may not exist a
=
solution which satisfies
the capacity constraint.
2 3 4 Then, ...
2
3 1 add one more vehicle!
add two more nodes to the family
of depot and the arcs between
the nodes and all the other nodes.
5
23. 3-3: Constructing a Feasible Solution
Each Delivery Route on the Original Graph (Feasible!)
1 1 1
(2,2) (2,2) (2,2) (2,2) (2,2) (2,2)
(1,3) (1,3) (1,3)
2 3 4 2 3 4 2 3 4
(3,2)
(3,3) (3,1) (3,1)
1 5 2 5 3 5
1 1 : served arcs
(2,2) (2,2) (2,2) (2,2) : passed arcs
2
(1,3)
3
(1,3)
4 2 3 4
All the routes of vehicles
satisfy the capacity constraint,
(3,3)
(3,1) then we obtained ...
4 5 5 5 a feasible solution !
24. 3-3: Constructing a Feasible Solution
How to Obtain an Optimal Solution?
An example of a search tree
1
U:
LC 2
U: 3
LC U: the early stage
LC
feasible
A feasible solution with the
minimum objective value is feasible
an optimal solution !
25. 4: Computational Experiments
Computing Environment and Instances
Environment: We used following 6 workstations connected by ether
net.
Machine: TOSHIBA SPARC LT In 6 workstations, ...
CPU: SPARC
Clock: 25MHz
Master process: 1 workstation
Slave processes: 1 process on a WS 1, 3, 5
workstations
No processes of other users were running15 demand arcs.
Instances: We solved 20 instances with on all the workstations.
In 20 instances, ...
Consideration: The number of subproblems when we used 1 workstation
as a slave processor is more over 1000. 6 instances.
27. 4: Computational Experiments
The Effects on the Computing Times
35000
H d: 1
ybri
30000 H d: 3
ybri
H d: 5
ybri
25000 D h: 1
ept
20000 D h: 3
ept
D h: 5
ept
15000 Bound: 1
Bound: 3
10000
Bound5
T g n t up m C
5000
o
0
N 1
o. N 2
o. N 3
o. N 4
o. N 5
o. N 6
o.
i
Problem No.
28. 4: Computational Experiments
The Effects on the Computing Times
Hybrid Depth First Best Bound
18.9 65.1
14. 00 14. 00 27.1 14. 00
12. 00 12. 00 12. 00
10. 00 10. 00 10. 00 N 1
o.
N 2
o.
8. 00 8. 00 8. 00 N 3
o.
6. 00 6. 00 6. 00 N 4
o.
N 5
o.
4. 00 4. 00 4. 00 N 6
o.
i t a R pudee pS
2. 00 2. 00 2. 00
0. 00 0. 00 0. 00
1LCU 3LCU 5LCU 1LCU 3LCU 5LCU 1LCU 3LCU 5LCU
Number of LCUs Number of LCUs Number of LCUs
29. 4: Computational Experiments
The Effects on the Number of Subproblems
Hybrid Depth First Best Bound
2. 00 2. 00 2. 00
1. 80 1. 80 1. 80
1. 60 1. 60 1. 60
1. 40 1. 40 1. 40 No. 1
1. 20 No. 2
1. 20 1. 20
No. 3
1. 00 1. 00 1. 00
No. 4
0. 80 0. 80 0. 80
No. 5
0. 60 0. 60 0. 60 No. 6
0. 40 0. 40 0. 40
0. 20 0. 20 0. 20
a Res aerc nI
re b m N
0. 00 0. 00 0. 00
u
1LCU 3LCU 5LCU 1LCU 3LCU 5LCU 1LCU 3LCU 5LCU
Number of LCUs Number of LCUs Number of LCUs
30. 5: Conclusion
The Results of the Study
We developed and implemented a new algorithm for
the capacitated arc routing problem.
The results
of the study We could obtain an optimal solutions to 20 instances.
We considered the computing results and verified the
effect of parallelization.
‘‘The 1995 Spring National Conference of ORSJ,’’
Presentations The Operations Research Society of Japan, Mar. 1995.
of the study ‘‘The Manthly Research Meeting of RAMP,’’
Research Association of Mathematical Programming, Sep. 1995.