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| faster algorithms via approximation theory: Faster Algorithms Via Approximation Theory Sushant Sachdeva, Nisheeth K. Vishnoi, 2014 This monograph presents ideas and techniques from approximation theory for approximating functions such as xs; x-1 and e-x, and demonstrates how these results play a crucial role in the design of fast algorithms for problems which are increasingly relevant. The key lies in the fact that such results imply faster ways to compute primitives such as Asv, A-1v, exp(-A)v, Eigenvalues, and Eigenvectors, which are fundamental to many spectral algorithms. Indeed, many fast algorithms reduce to the computation of such primitives, which have proved useful for speeding up several fundamental computations such as random walk simulation, graph partitioning, and solving systems of linear equations. |
| faster algorithms via approximation theory: Faster Algorithms Via Approximation Theory Sushant Sachdeva, Nisheeth K. Vishnoi, 2014-03-28 Faster Algorithms via Approximation Theory illustrates how classical and modern techniques from approximation theory play a crucial role in obtaining results that are relevant to the emerging theory of fast algorithms. The key lies in the fact that such results imply faster ways to approximate primitives such as products of matrix functions with vectors and, to compute matrix eigenvalues and eigenvectors, which are fundamental to many spectral algorithms. The first half of the book is devoted to the ideas and results from approximation theory that are central, elegant, and may have wider applicability in theoretical computer science. These include not only techniques relating to polynomial approximations but also those relating to approximations by rational functions and beyond. The remaining half illustrates a variety of ways that these results can be used to design fast algorithms. Faster Algorithms via Approximation Theory is self-contained and should be of interest to researchers and students in theoretical computer science, numerical linear algebra, and related areas. |
| faster algorithms via approximation theory: Approximation Theory and Approximation Practice, Extended Edition Lloyd N. Trefethen, 2019-01-01 This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the fields most important ideas and results. Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online. The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation. This textbook is appropriate for advanced undergraduate or graduate students who have an understanding of numerical analysis and complex analysis. It is also appropriate for seasoned mathematicians who use MATLAB. |
| faster algorithms via approximation theory: Approximation Theory and Algorithms for Data Analysis Armin Iske, 2018-12-14 This textbook offers an accessible introduction to the theory and numerics of approximation methods, combining classical topics of approximation with recent advances in mathematical signal processing, and adopting a constructive approach, in which the development of numerical algorithms for data analysis plays an important role. The following topics are covered: * least-squares approximation and regularization methods * interpolation by algebraic and trigonometric polynomials * basic results on best approximations * Euclidean approximation * Chebyshev approximation * asymptotic concepts: error estimates and convergence rates * signal approximation by Fourier and wavelet methods * kernel-based multivariate approximation * approximation methods in computerized tomography Providing numerous supporting examples, graphical illustrations, and carefully selected exercises, this textbook is suitable for introductory courses, seminars, and distance learning programs on approximation for undergraduate students. |
| faster algorithms via approximation theory: Approximation Theory XV: San Antonio 2016 Gregory E. Fasshauer, Larry L. Schumaker, 2017-07-19 These proceedings are based on papers presented at the international conference Approximation Theory XV, which was held May 22–25, 2016 in San Antonio, Texas. The conference was the fifteenth in a series of meetings in Approximation Theory held at various locations in the United States, and was attended by 146 participants. The book contains longer survey papers by some of the invited speakers covering topics such as compressive sensing, isogeometric analysis, and scaling limits of polynomials and entire functions of exponential type. The book also includes papers on a variety of current topics in Approximation Theory drawn from areas such as advances in kernel approximation with applications, approximation theory and algebraic geometry, multivariate splines for applications, practical function approximation, approximation of PDEs, wavelets and framelets with applications, approximation theory in signal processing, compressive sensing, rational interpolation, spline approximation in isogeometric analysis, approximation of fractional differential equations, numerical integration formulas, and trigonometric polynomial approximation. |
| faster algorithms via approximation theory: Approximation Theory Carl De Boor, American Mathematical Society, 1986-12-31 The papers in this book, first presented at a 1986 AMS Short Course, give a brief introduction to approximation theory and some of its current areas of active research, both theoretical and applied. The first lecture describes and illustrates the basic concerns of the field. Topics highlighted in the other lectures include the following: approximation in the complex domain, $N$-width, optimal recovery, interpolation, algorithms for approximation, and splines, with a strong emphasis on a multivariate setting for the last three topics. The book is aimed at mathematicians interested in an introduction to areas of current research and to engineers and scientists interested in exploring the field for possible applications to their own fields. The book is best understood by those with a standard first graduate course in real and complex analysis, but some of the presentations are accessible with the minimal requirements of advanced calculus and linear algebra. |
| faster algorithms via approximation theory: Fast and approximate computation of Laplace and Fourier transforms Ines Melzer, 2016-03-20 In this thesis, we treat the computation of transforms with asymptotically smooth and oscillatory kernels. We introduce the discrete Laplace transform in a modern form including a generalization to more general kernel functions. These more general kernels lead to specific function transforms. Moreover, we treat the butterfly fast Fourier transform. Based on a local error analysis, we develop a rigorous error analysis for the whole butterfly scheme. In the final part of the thesis, the Laplace and Fourier transform are combined to a fast Fourier transform for nonequispaced complex evaluation nodes. All theoretical results on accuracy and computational complexity are illustrated by numerical experiments. |
| faster algorithms via approximation theory: Research in Progress , 1980 |
| faster algorithms via approximation theory: Geometric Approximation Algorithms Sariel Har-Peled, 2011 Exact algorithms for dealing with geometric objects are complicated, hard to implement in practice, and slow. Over the last 20 years a theory of geometric approximation algorithms has emerged. These algorithms tend to be simple, fast, and more robust than their exact counterparts. This book is the first to cover geometric approximation algorithms in detail. In addition, more traditional computational geometry techniques that are widely used in developing such algorithms, like sampling, linear programming, etc., are also surveyed. Other topics covered include approximate nearest-neighbor search, shape approximation, coresets, dimension reduction, and embeddings. The topics covered are relatively independent and are supplemented by exercises. Close to 200 color figures are included in the text to illustrate proofs and ideas. |
| faster algorithms via approximation theory: Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms , 2003-01-01 From the January 2003 symposium come just over 100 papers addressing a range of topics related to discrete algorithms. Examples of topics covered include packing Steiner trees, counting inversions in lists, directed scale-free graphs, quantum property testing, and improved results for directed multicut. The papers were not formally refereed, but attempts were made to verify major results. Annotation (c)2003 Book News, Inc., Portland, OR (booknews.com) |
| faster algorithms via approximation theory: Handbook of Approximation Algorithms and Metaheuristics Teofilo F. Gonzalez, 2007-05-15 Delineating the tremendous growth in this area, the Handbook of Approximation Algorithms and Metaheuristics covers fundamental, theoretical topics as well as advanced, practical applications. It is the first book to comprehensively study both approximation algorithms and metaheuristics. Starting with basic approaches, the handbook presents the methodologies to design and analyze efficient approximation algorithms for a large class of problems, and to establish inapproximability results for another class of problems. It also discusses local search, neural networks, and metaheuristics, as well as multiobjective problems, sensitivity analysis, and stability. After laying this foundation, the book applies the methodologies to classical problems in combinatorial optimization, computational geometry, and graph problems. In addition, it explores large-scale and emerging applications in networks, bioinformatics, VLSI, game theory, and data analysis. Undoubtedly sparking further developments in the field, this handbook provides the essential techniques to apply approximation algorithms and metaheuristics to a wide range of problems in computer science, operations research, computer engineering, and economics. Armed with this information, researchers can design and analyze efficient algorithms to generate near-optimal solutions for a wide range of computational intractable problems. |
| faster algorithms via approximation theory: Approximation Algorithms Vijay V. Vazirani, 2002-12-05 Covering the basic techniques used in the latest research work, the author consolidates progress made so far, including some very recent and promising results, and conveys the beauty and excitement of work in the field. He gives clear, lucid explanations of key results and ideas, with intuitive proofs, and provides critical examples and numerous illustrations to help elucidate the algorithms. Many of the results presented have been simplified and new insights provided. Of interest to theoretical computer scientists, operations researchers, and discrete mathematicians. |
| faster algorithms via approximation theory: Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques Prasad Raghavendra, Sofya Raskhodnikova, Klaus Jansen, José D.P. Rolim, 2013-08-16 This book constitutes the proceedings of the 16th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2013, and the 17th International Workshop on Randomization and Computation, RANDOM 2013, held in August 2013 in the USA. The total of 48 carefully reviewed and selected papers presented in this volume consist of 23 APPROX papers selected out of 46 submissions, and 25 RANDOM papers selected out of 52 submissions. APPROX 2013 focuses on algorithmic and complexity theoretic issues relevant to the development of efficient approximate solutions to computationally difficult problems, while RANDOM 2013 focuses on applications of randomness to computational and combinatorial problems. |
| faster algorithms via approximation theory: The Design of Approximation Algorithms David P. Williamson, David B. Shmoys, 2011-04-26 Discrete optimization problems are everywhere, from traditional operations research planning (scheduling, facility location and network design); to computer science databases; to advertising issues in viral marketing. Yet most such problems are NP-hard; unless P = NP, there are no efficient algorithms to find optimal solutions. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first section is devoted to a single algorithmic technique applied to several different problems, with more sophisticated treatment in the second section. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithm courses, it will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems. |
| faster algorithms via approximation theory: Proceedings of the Seventeenth Annual ACM-SIAM Symposium on Discrete Algorithms SIAM Activity Group on Discrete Mathematics, Association for Computing Machinery, Society for Industrial and Applied Mathematics, 2006-01-01 Symposium held in Miami, Florida, January 22–24, 2006.This symposium is jointly sponsored by the ACM Special Interest Group on Algorithms and Computation Theory and the SIAM Activity Group on Discrete Mathematics.Contents Preface; Acknowledgments; Session 1A: Confronting Hardness Using a Hybrid Approach, Virginia Vassilevska, Ryan Williams, and Shan Leung Maverick Woo; A New Approach to Proving Upper Bounds for MAX-2-SAT, Arist Kojevnikov and Alexander S. Kulikov, Measure and Conquer: A Simple O(20.288n) Independent Set Algorithm, Fedor V. Fomin, Fabrizio Grandoni, and Dieter Kratsch; A Polynomial Algorithm to Find an Independent Set of Maximum Weight in a Fork-Free Graph, Vadim V. Lozin and Martin Milanic; The Knuth-Yao Quadrangle-Inequality Speedup is a Consequence of Total-Monotonicity, Wolfgang W. Bein, Mordecai J. Golin, Larry L. Larmore, and Yan Zhang; Session 1B: Local Versus Global Properties of Metric Spaces, Sanjeev Arora, László Lovász, Ilan Newman, Yuval Rabani, Yuri Rabinovich, and Santosh Vempala; Directed Metrics and Directed Graph Partitioning Problems, Moses Charikar, Konstantin Makarychev, and Yury Makarychev; Improved Embeddings of Graph Metrics into Random Trees, Kedar Dhamdhere, Anupam Gupta, and Harald Räcke; Small Hop-diameter Sparse Spanners for Doubling Metrics, T-H. Hubert Chan and Anupam Gupta; Metric Cotype, Manor Mendel and Assaf Naor; Session 1C: On Nash Equilibria for a Network Creation Game, Susanne Albers, Stefan Eilts, Eyal Even-Dar, Yishay Mansour, and Liam Roditty; Approximating Unique Games, Anupam Gupta and Kunal Talwar; Computing Sequential Equilibria for Two-Player Games, Peter Bro Miltersen and Troels Bjerre Sørensen; A Deterministic Subexponential Algorithm for Solving Parity Games, Marcin Jurdzinski, Mike Paterson, and Uri Zwick; Finding Nucleolus of Flow Game, Xiaotie Deng, Qizhi Fang, and Xiaoxun Sun, Session 2: Invited Plenary Abstract: Predicting the “Unpredictable”, Rakesh V. Vohra, Northwestern University; Session 3A: A Near-Tight Approximation Lower Bound and Algorithm for the Kidnapped Robot Problem, Sven Koenig, Apurva Mudgal, and Craig Tovey; An Asymptotic Approximation Algorithm for 3D-Strip Packing, Klaus Jansen and Roberto Solis-Oba; Facility Location with Hierarchical Facility Costs, Zoya Svitkina and Éva Tardos; Combination Can Be Hard: Approximability of the Unique Coverage Problem, Erik D. Demaine, Uriel Feige, Mohammad Taghi Hajiaghayi, and Mohammad R. Salavatipour; Computing Steiner Minimum Trees in Hamming Metric, Ernst Althaus and Rouven Naujoks; Session 3B: Robust Shape Fitting via Peeling and Grating Coresets, Pankaj K. Agarwal, Sariel Har-Peled, and Hai Yu; Tightening Non-Simple Paths and Cycles on Surfaces, Éric Colin de Verdière and Jeff Erickson; Anisotropic Surface Meshing, Siu-Wing Cheng, Tamal K. Dey, Edgar A. Ramos, and Rephael Wenger; Simultaneous Diagonal Flips in Plane Triangulations, Prosenjit Bose, Jurek Czyzowicz, Zhicheng Gao, Pat Morin, and David R. Wood; Morphing Orthogonal Planar Graph Drawings, Anna Lubiw, Mark Petrick, and Michael Spriggs; Session 3C: Overhang, Mike Paterson and Uri Zwick; On the Capacity of Information Networks, Micah Adler, Nicholas J. A. Harvey, Kamal Jain, Robert Kleinberg, and April Rasala Lehman; Lower Bounds for Asymmetric Communication Channels and Distributed Source Coding, Micah Adler, Erik D. Demaine, Nicholas J. A. Harvey, and Mihai Patrascu; Self-Improving Algorithms, Nir Ailon, Bernard Chazelle, Seshadhri Comandur, and Ding Liu; Cake Cutting Really is Not a Piece of Cake, Jeff Edmonds and Kirk Pruhs; Session 4A: Testing Triangle-Freeness in General Graphs, Noga Alon, Tali Kaufman, Michael Krivelevich, and Dana Ron; Constraint Solving via Fractional Edge Covers, Martin Grohe and Dániel Marx; Testing Graph Isomorphism, Eldar Fischer and Arie Matsliah; Efficient Construction of Unit Circular-Arc Models, Min Chih Lin and Jayme L. Szwarcfiter, On The Chromatic Number of Some Geometric Hypergraphs, Shakhar Smorodinsky; Session 4B: A Robust Maximum Completion Time Measure for Scheduling, Moses Charikar and Samir Khuller; Extra Unit-Speed Machines are Almost as Powerful as Speedy Machines for Competitive Flow Time Scheduling, Ho-Leung Chan, Tak-Wah Lam, and Kin-Shing Liu; Improved Approximation Algorithms for Broadcast Scheduling, Nikhil Bansal, Don Coppersmith, and Maxim Sviridenko; Distributed Selfish Load Balancing, Petra Berenbrink, Tom Friedetzky, Leslie Ann Goldberg, Paul Goldberg, Zengjian Hu, and Russell Martin; Scheduling Unit Tasks to Minimize the Number of Idle Periods: A Polynomial Time Algorithm for Offline Dynamic Power Management, Philippe Baptiste; Session 4C: Rank/Select Operations on Large Alphabets: A Tool for Text Indexing, Alexander Golynski, J. Ian Munro, and S. Srinivasa Rao; O(log log n)-Competitive Dynamic Binary Search Trees, Chengwen Chris Wang, Jonathan Derryberry, and Daniel Dominic Sleator; The Rainbow Skip Graph: A Fault-Tolerant Constant-Degree Distributed Data Structure, Michael T. Goodrich, Michael J. Nelson, and Jonathan Z. Sun; Design of Data Structures for Mergeable Trees, Loukas Georgiadis, Robert E. Tarjan, and Renato F. Werneck; Implicit Dictionaries with O(1) Modifications per Update and Fast Search, Gianni Franceschini and J. Ian Munro; Session 5A: Sampling Binary Contingency Tables with a Greedy Start, Ivona Bezáková, Nayantara Bhatnagar, and Eric Vigoda; Asymmetric Balanced Allocation with Simple Hash Functions, Philipp Woelfel; Balanced Allocation on Graphs, Krishnaram Kenthapadi and Rina Panigrahy; Superiority and Complexity of the Spaced Seeds, Ming Li, Bin Ma, and Louxin Zhang; Solving Random Satisfiable 3CNF Formulas in Expected Polynomial Time, Michael Krivelevich and Dan Vilenchik; Session 5B: Analysis of Incomplete Data and an Intrinsic-Dimension Helly Theorem, Jie Gao, Michael Langberg, and Leonard J. Schulman; Finding Large Sticks and Potatoes in Polygons, Olaf Hall-Holt, Matthew J. Katz, Piyush Kumar, Joseph S. B. Mitchell, and Arik Sityon; Randomized Incremental Construction of Three-Dimensional Convex Hulls and Planar Voronoi Diagrams, and Approximate Range Counting, Haim Kaplan and Micha Sharir; Vertical Ray Shooting and Computing Depth Orders for Fat Objects, Mark de Berg and Chris Gray; On the Number of Plane Graphs, Oswin Aichholzer, Thomas Hackl, Birgit Vogtenhuber, Clemens Huemer, Ferran Hurtado, and Hannes Krasser; Session 5C: All-Pairs Shortest Paths for Unweighted Undirected Graphs in o(mn) Time, Timothy M. Chan; An O(n log n) Algorithm for Maximum st-Flow in a Directed Planar Graph, Glencora Borradaile and Philip Klein; A Simple GAP-Canceling Algorithm for the Generalized Maximum Flow Problem, Mateo Restrepo and David P. Williamson; Four Point Conditions and Exponential Neighborhoods for Symmetric TSP, Vladimir Deineko, Bettina Klinz, and Gerhard J. Woeginger; Upper Degree-Constrained Partial Orientations, Harold N. Gabow; Session 7A: On the Tandem Duplication-Random Loss Model of Genome Rearrangement, Kamalika Chaudhuri, Kevin Chen, Radu Mihaescu, and Satish Rao; Reducing Tile Complexity for Self-Assembly Through Temperature Programming, Ming-Yang Kao and Robert Schweller; Cache-Oblivious String Dictionaries, Gerth Stølting Brodal and Rolf Fagerberg; Cache-Oblivious Dynamic Programming, Rezaul Alam Chowdhury and Vijaya Ramachandran; A Computational Study of External-Memory BFS Algorithms, Deepak Ajwani, Roman Dementiev, and Ulrich Meyer; Session 7B: Tight Approximation Algorithms for Maximum General Assignment Problems, Lisa Fleischer, Michel X. Goemans, Vahab S. Mirrokni, and Maxim Sviridenko; Approximating the k-Multicut Problem, Daniel Golovin, Viswanath Nagarajan, and Mohit Singh; The Prize-Collecting Generalized Steiner Tree Problem Via A New Approach Of Primal-Dual Schema, Mohammad Taghi Hajiaghayi and Kamal Jain; 8/7-Approximation Algorithm for (1,2)-TSP, Piotr Berman and Marek Karpinski; Improved Lower and Upper Bounds for Universal TSP in Planar Metrics, Mohammad T. Hajiaghayi, Robert Kleinberg, and Tom Leighton; Session 7C: Leontief Economies Encode NonZero Sum Two-Player Games, B. Codenotti, A. Saberi, K. Varadarajan, and Y. Ye; Bottleneck Links, Variable Demand, and the Tragedy of the Commons, Richard Cole, Yevgeniy Dodis, and Tim Roughgarden; The Complexity of Quantitative Concurrent Parity Games, Krishnendu Chatterjee, Luca de Alfaro, and Thomas A. Henzinger; Equilibria for Economies with Production: Constant-Returns Technologies and Production Planning Constraints, Kamal Jain and Kasturi Varadarajan; Session 8A: Approximation Algorithms for Wavelet Transform Coding of Data Streams, Sudipto Guha and Boulos Harb; Simpler Algorithm for Estimating Frequency Moments of Data Streams, Lakshimath Bhuvanagiri, Sumit Ganguly, Deepanjan Kesh, and Chandan Saha; Trading Off Space for Passes in Graph Streaming Problems, Camil Demetrescu, Irene Finocchi, and Andrea Ribichini; Maintaining Significant Stream Statistics over Sliding Windows, L.K. Lee and H.F. Ting; Streaming and Sublinear Approximation of Entropy and Information Distances, Sudipto Guha, Andrew McGregor, and Suresh Venkatasubramanian; Session 8B: FPTAS for Mixed-Integer Polynomial Optimization with a Fixed Number of Variables, J. A. De Loera, R. Hemmecke, M. Köppe, and R. Weismantel; Linear Programming and Unique Sink Orientations, Bernd Gärtner and Ingo Schurr; Generating All Vertices of a Polyhedron is Hard, Leonid Khachiyan, Endre Boros, Konrad Borys, Khaled Elbassioni, and Vladimir Gurvich; A Semidefinite Programming Approach to Tensegrity Theory and Realizability of Graphs, Anthony Man-Cho So and Yinyu Ye; Ordering by Weighted Number of Wins Gives a Good Ranking for Weighted Tournaments, Don Coppersmith, Lisa Fleischer, and Atri Rudra; Session 8C: Weighted Isotonic Regression under L1 Norm, Stanislav Angelov, Boulos Harb, Sampath Kannan, and Li-San Wang; Oblivious String Embeddings and Edit Distance Approximations, Tugkan Batu, Funda Ergun, and Cenk Sahinalp0898716012\\This comprehensive book not only introduces the C and C++ programming languages but also shows how to use them in the numerical solution of partial differential equations (PDEs). It leads the reader through the entire solution process, from the original PDE, through the discretization stage, to the numerical solution of the resulting algebraic system. The well-debugged and tested code segments implement the numerical methods efficiently and transparently. Basic and advanced numerical methods are introduced and implemented easily and efficiently in a unified object-oriented approach. |
| faster algorithms via approximation theory: The Design of Competitive Online Algorithms Via a Primal-Dual Approach Niv Buchbinder, Joseph Naor, 2009 Extends the primal-dual method to the setting of online algorithms, and shows its applicability to a wide variety of fundamental problems. |
| faster algorithms via approximation theory: The Design of Approximation Algorithms David P. Williamson, David B. Shmoys, 2011-04-26 Discrete optimization problems are everywhere, from traditional operations research planning problems, such as scheduling, facility location, and network design; to computer science problems in databases; to advertising issues in viral marketing. Yet most such problems are NP-hard. Thus unless P = NP, there are no efficient algorithms to find optimal solutions to such problems. This book shows how to design approximation algorithms: efficient algorithms that find provably near-optimal solutions. The book is organized around central algorithmic techniques for designing approximation algorithms, including greedy and local search algorithms, dynamic programming, linear and semidefinite programming, and randomization. Each chapter in the first part of the book is devoted to a single algorithmic technique, which is then applied to several different problems. The second part revisits the techniques but offers more sophisticated treatments of them. The book also covers methods for proving that optimization problems are hard to approximate. Designed as a textbook for graduate-level algorithms courses, the book will also serve as a reference for researchers interested in the heuristic solution of discrete optimization problems. |
| faster algorithms via approximation theory: Theory and Applications of Models of Computation Manindra Agrawal, Barry S. Cooper, Angsheng Li, 2012-05-04 This book constitutes the refereed proceedings of the 9th International Conference on Theory and Applications of Models of Computation, TAMC 2012, held in Beijing, China, in May 2012. The conference was combined with the Turing Lectures 2012, dedicated to celebrating Alan Turing’s unique impact on mathematics, computing, computer science, informatics, morphogenesis, philosophy, and the wider scientific world. Eight Turing Lectures were given at the TAMC 2012. The 40 revised full papers presented together with invited talks were carefully reviewed and selected from 86 submissions. The papers address 4 special sessions at TAMC 2012 which were algorithms and information in networks, complexity and cryptography, models of computing and networking, programming and verification. |
| faster algorithms via approximation theory: Algorithms – ESA 2005 Gerth S. Brodal, Stefano Leonardi, 2005-09-19 This book constitutes the refereed proceedings of the 13th Annual European Symposium on Algorithms, ESA 2005, held in Palma de Mallorca, Spain, in September 2005 in the context of the combined conference ALGO 2005. The 75 revised full papers presented together with abstracts of 3 invited lectures were carefully reviewed and selected from 244 submissions. The papers address all current issues in algorithmics reaching from design and mathematical issues over real-world applications in various fields up to engineering and analysis of algorithms. |
| faster algorithms via approximation theory: Approximation and Online Algorithms Evripidis Bampis, Ola Svensson, 2015-04-22 This book constitutes the thoroughly refereed post-workshop proceedings of the 12th International Workshop on Approximation and Online Algorithms, WAOA 2014, held in Wrocław, Poland, in September 2014 as part of ALGO 2014. The 22 revised full papers presented were carefully reviewed and selected from 49 submissions. They cover a wide range of topics such as coloring and partitioning, competitive analysis, network design, packing and covering, paradigms for design and analysis of approximation and online algorithms, randomization techniques, real-world applications, and scheduling problems. |
| faster algorithms via approximation theory: Numerical Fourier Analysis Gerlind Plonka, Daniel Potts, Gabriele Steidl, Manfred Tasche, 2023-11-08 New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods. To address this growing need, this monograph combines mathematical theory and numerical algorithms to offer a unified and self-contained presentation of Fourier analysis. The first four chapters of the text serve as an introduction to classical Fourier analysis in the univariate and multivariate cases, including the discrete Fourier transforms, providing the necessary background for all further chapters. Next, chapters explore the construction and analysis of corresponding fast algorithms in the one- and multidimensional cases. The well-known fast Fourier transforms (FFTs) are discussed, as well as recent results on the construction of the nonequispaced FFTs, high-dimensional FFTs on special lattices, and sparse FFTs. An additional chapter is devoted to discrete trigonometric transforms and Chebyshev expansions. The final two chapters consider various applications of numerical Fourier methods for improved function approximation, including Prony methods for the recovery of structured functions. This new edition has been revised and updated throughout, featuring new material on a new Fourier approach to the ANOVA decomposition of high-dimensional trigonometric polynomials; new research results on the approximation errors of the nonequispaced fast Fourier transform based on special window functions; and the recently developed ESPIRA algorithm for recovery of exponential sums, among others. Numerical Fourier Analysis will be of interest to graduate students and researchers in applied mathematics, physics, computer science, engineering, and other areas where Fourier methods play an important role in applications. |
| faster algorithms via approximation theory: Fast Algorithms for Structured Matrices Vadim Olshevsky, 2003 One of the best known fast computational algorithms is the fast Fourier transform method. Its efficiency is based mainly on the special structure of the discrete Fourier transform matrix. Recently, many other algorithms of this type were discovered, and the theory of structured matrices emerged. This volume contains 22 survey and research papers devoted to a variety of theoretical and practical aspects of the design of fast algorithms for structured matrices and related issues. Included are several papers containing various affirmative and negative results in this direction. The theory of rational interpolation is one of the excellent sources providing intuition and methods to design fast algorithms. The volume contains several computational and theoretical papers on the topic. There are several papers on new applications of structured matrices, e.g., to the design of fast decoding algorithms, computing state-space realizations, relations to Lie algebras, unconstrained optimization, solving matrix equations, etc. The book is suitable for mathematicians, engineers, and numerical analysts who design, study, and use fast computational algorithms based on the theory of structured matrices. |
| faster algorithms via approximation theory: Fast Reliable Algorithms for Matrices with Structure T. Kailath, A. H. Sayed, 1999-01-01 This book is the first to pay special attention to the combined issues of speed and numerical reliability in algorithm development. These two requirements have often been regarded as competitive, so much so that the design of fast and numerically reliable algorithms for large-scale structured systems of linear equations, in many cases, remains a significant open issue. Fast Reliable Algorithms for Matrices with Structure helps bridge this gap by providing the reader with recent contributions written by leading experts in the field. The authors deal with both the theory and the practice of fast numerical algorithms for large-scale structured linear systems. Each chapter covers in detail different aspects of the most recent trends in the theory of fast algorithms, with emphasis on implementation and application issues. Both direct and iterative methods are covered. This book is not merely a collection of articles. The editors have gone to considerable lengths to blend the individual papers into a consistent presentation. Each chapter exposes the reader to some of the most recent research while providing enough background material to put the work into proper context. |
| faster algorithms via approximation theory: Integer Programming and Combinatorial Optimization Andrea Lodi, Viswanath Nagarajan, 2019-05-02 This book constitutes the refereed proceedings of the 20th International Conference on Integer Programming and Combinatorial Optimization, IPCO 2019, held in Ann Arbor, MI, USA, in May 2019. The 33 full versions of extended abstracts presented were carefully reviewed and selected from 114 submissions. The conference is a forum for researchers and practitioners working on various aspects of integer programming and combinatorial optimization. The aim is to present recent developments in theory, computation, and applications in these areas. |
| faster algorithms via approximation theory: Algorithms for Convex Optimization Nisheeth K. Vishnoi, 2021-10-07 In the last few years, Algorithms for Convex Optimization have revolutionized algorithm design, both for discrete and continuous optimization problems. For problems like maximum flow, maximum matching, and submodular function minimization, the fastest algorithms involve essential methods such as gradient descent, mirror descent, interior point methods, and ellipsoid methods. The goal of this self-contained book is to enable researchers and professionals in computer science, data science, and machine learning to gain an in-depth understanding of these algorithms. The text emphasizes how to derive key algorithms for convex optimization from first principles and how to establish precise running time bounds. This modern text explains the success of these algorithms in problems of discrete optimization, as well as how these methods have significantly pushed the state of the art of convex optimization itself. |
| faster algorithms via approximation theory: Research in Progress Between ... and United States. Army Research Office, 1978 |
| faster algorithms via approximation theory: Network Flow Algorithms David P. Williamson, 2019-09-05 Network flow theory has been used across a number of disciplines, including theoretical computer science, operations research, and discrete math, to model not only problems in the transportation of goods and information, but also a wide range of applications from image segmentation problems in computer vision to deciding when a baseball team has been eliminated from contention. This graduate text and reference presents a succinct, unified view of a wide variety of efficient combinatorial algorithms for network flow problems, including many results not found in other books. It covers maximum flows, minimum-cost flows, generalized flows, multicommodity flows, and global minimum cuts and also presents recent work on computing electrical flows along with recent applications of these flows to classical problems in network flow theory. |
| faster algorithms via approximation theory: Encyclopedia of Algorithms Ming-Yang Kao, 2008-08-06 One of Springer’s renowned Major Reference Works, this awesome achievement provides a comprehensive set of solutions to important algorithmic problems for students and researchers interested in quickly locating useful information. This first edition of the reference focuses on high-impact solutions from the most recent decade, while later editions will widen the scope of the work. All entries have been written by experts, while links to Internet sites that outline their research work are provided. The entries have all been peer-reviewed. This defining reference is published both in print and on line. |
| faster algorithms via approximation theory: A Mathematical Introduction to Compressive Sensing Simon Foucart, Holger Rauhut, 2013-08-13 At the intersection of mathematics, engineering, and computer science sits the thriving field of compressive sensing. Based on the premise that data acquisition and compression can be performed simultaneously, compressive sensing finds applications in imaging, signal processing, and many other domains. In the areas of applied mathematics, electrical engineering, and theoretical computer science, an explosion of research activity has already followed the theoretical results that highlighted the efficiency of the basic principles. The elegant ideas behind these principles are also of independent interest to pure mathematicians. A Mathematical Introduction to Compressive Sensing gives a detailed account of the core theory upon which the field is build. With only moderate prerequisites, it is an excellent textbook for graduate courses in mathematics, engineering, and computer science. It also serves as a reliable resource for practitioners and researchers in these disciplines who want to acquire a careful understanding of the subject. A Mathematical Introduction to Compressive Sensing uses a mathematical perspective to present the core of the theory underlying compressive sensing. |
| faster algorithms via approximation theory: Meshfree Approximation Methods with MATLAB Gregory E. Fasshauer, 2007 Meshfree approximation methods are a relatively new area of research. This book provides the salient theoretical results needed for a basic understanding of meshfree approximation methods. It places emphasis on a hands-on approach that includes MATLAB routines for all basic operations. |
| faster algorithms via approximation theory: WALCOM: Algorithms and Computation NAOKI KATOH, Amit Kumar, 2011-02-11 This book constitutes the proceedings of the 5th International Workshop on Algorithms and Computation, WALCOM 2011, held in New Delhi, India, in February 2011. The 20 papers presented in this volume were carefully reviewed and selected from 57 submissions. The papers are grouped in topical sections on approximation algorithms, hardness, algorithm engineering, computational geometry, string algorithms, and graph algorithms. |
| faster algorithms via approximation theory: Distributed Computing Marcos K. Aguilera, 2012-10-14 This book constitutes the refereed proceedings of the 26th International Symposium on Distributed Computing, DISC 2012, held in Salvador, Brazil, in October 2012. The 27 revised full papers presented together with 24 brief announcements were carefully reviewed and selected from 119 submissions. The papers are organized in topical sections on shared memory, mobile agents and overlay networks, wireless and multiple access channel networks, dynamic networks, distributed graph algorithms, wireless and loosely connected networks, robots, and lower bounds and separation. |
| faster algorithms via approximation theory: FST TCS 2000: Foundations of Software Technology and Theoretical Science Sanjiv Kapoor, 2000-11-29 This book constitutes the refereed proceedings of the 20th international Conference on Foundations of Software Technology and Theoretical Computer Science, FST TCS 2000, held in New Delhi, India in December 2000. The 36 revised full papers presented were carefully reviewed and selected from a total of 141 submissions; also included are six invited papers. The volume provides broad coverage of the logical and mathematical foundations of computer science and spans the whole range of theoretical computer science. |
| faster algorithms via approximation theory: Combinatorial and Algorithmic Aspects of Networking Alejandro López-Ortiz, 2005-07-14 This book constitutes the refereed proceedings of the first workshop on Combinatorial and Algorithmic Aspects of Networking, held in Banff, Alberta, Canada in August 2004. The 12 revised full papers together with two invited papers presented were carefully reviewed and selected for inclusion in the book. The topics covered range from the web graph to game theory to string matching, all in the context of large-scale networks. This volume contains also 5 survey articles to round out the presentation and give a comprehensive introduction to the topic. |
| faster algorithms via approximation theory: Machine Learning, Optimization, and Data Science Giuseppe Nicosia, Panos Pardalos, Renato Umeton, Giovanni Giuffrida, Vincenzo Sciacca, 2020-01-03 This book constitutes the post-conference proceedings of the 5th International Conference on Machine Learning, Optimization, and Data Science, LOD 2019, held in Siena, Italy, in September 2019. The 54 full papers presented were carefully reviewed and selected from 158 submissions. The papers cover topics in the field of machine learning, artificial intelligence, reinforcement learning, computational optimization and data science presenting a substantial array of ideas, technologies, algorithms, methods and applications. |
| faster algorithms via approximation theory: Sampling Techniques for Supervised or Unsupervised Tasks Frédéric Ros, Serge Guillaume, 2019-10-26 This book describes in detail sampling techniques that can be used for unsupervised and supervised cases, with a focus on sampling techniques for machine learning algorithms. It covers theory and models of sampling methods for managing scalability and the “curse of dimensionality”, their implementations, evaluations, and applications. A large part of the book is dedicated to database comprising standard feature vectors, and a special section is reserved to the handling of more complex objects and dynamic scenarios. The book is ideal for anyone teaching or learning pattern recognition and interesting teaching or learning pattern recognition and is interested in the big data challenge. It provides an accessible introduction to the field and discusses the state of the art concerning sampling techniques for supervised and unsupervised task. Provides a comprehensive description of sampling techniques for unsupervised and supervised tasks; Describe implementation and evaluation of algorithms that simultaneously manage scalable problems and curse of dimensionality; Addresses the role of sampling in dynamic scenarios, sampling when dealing with complex objects, and new challenges arising from big data. This book represents a timely collection of state-of-the art research of sampling techniques, suitable for anyone who wants to become more familiar with these helpful techniques for tackling the big data challenge. M. Emre Celebi, Ph.D., Professor and Chair, Department of Computer Science, University of Central Arkansas In science the difficulty is not to have ideas, but it is to make them work From Carlo Rovelli |
| faster algorithms via approximation theory: Computer Analysis of Images and Patterns Vaclav Hlavac, Radim Sara, 1995-08-23 This book presents the proceedings of the Sixth International Conference on Computer Analysis of Images and Patterns, CAIP '95, held in Prague, Czech Republic in September 1995. The volume presents 61 full papers and 75 posters selected from a total of 262 submissions and thus gives a comprehensive view on the state-of-the-art in computer analysis of images and patterns, research, design, and advanced applications. The papers are organized in sections on invariants, segmentation and grouping, optical flow, model recovery and parameter estimation, low level vision, motion detection, structure and matching, active vision and shading, human face recognition, calibration, contour, and sessions on applications in diverse areas. |
| faster algorithms via approximation theory: Visions of DNA Nanotechnology at 40 for the Next 40 Nataša Jonoska, Erik Winfree, 2023-07-04 This open access book provides a unique and state-of-the-art view on DNA nanotechnology with an eye toward future developments. Intended as a tribute to Nadrian C. Seeman, who founded the field of DNA nanotechnology, the content is an exciting mixture of technical and non-technical material, reviews, tutorials, perspectives, new findings, and open questions. The book aims to inspire current researchers to sit back and think about the big picture, while also enticing new researchers to enter the field. Most of all, the book captures voices from a unique moment in time: 40 years after the publication of the first paper that envisioned DNA nanotechnology. From this vantage point, what are the untold stories, the unspoken concerns, the underlying fundamental issues, the overlooked opportunities, and the unifying grand challenges? What will help us see more clearly, see more creatively, or see farther? What is transpiring right now that could pave the way for the future? To address these questions, leading researchers have contributed 22 chapters, grouped into five sections: perspectives, chemistry and physics, structures, biochemical circuits, and spatial systems. This book will be an important reference point in the field of DNA nanotechnology, both for established researchers looking to take stock of the field and its future, and for newcomers such as graduate students and researchers in other fields who are beginning to appreciate the power and applicability of its methods. |
| faster algorithms via approximation theory: Computer Vision – ECCV 2012 Andrew Fitzgibbon, Svetlana Lazebnik, Pietro Perona, Yoichi Sato, Cordelia Schmid, 2012-09-26 The seven-volume set comprising LNCS volumes 7572-7578 constitutes the refereed proceedings of the 12th European Conference on Computer Vision, ECCV 2012, held in Florence, Italy, in October 2012. The 408 revised papers presented were carefully reviewed and selected from 1437 submissions. The papers are organized in topical sections on geometry, 2D and 3D shape, 3D reconstruction, visual recognition and classification, visual features and image matching, visual monitoring: action and activities, models, optimisation, learning, visual tracking and image registration, photometry: lighting and colour, and image segmentation. |
| faster algorithms via approximation theory: Explorations in the Mathematics of Data Science Simon Foucart, Stephan Wojtowytsch, 2024-09-12 This edited volume reports on the recent activities of the new Center for Approximation and Mathematical Data Analytics (CAMDA) at Texas A&M University. Chapters are based on talks from CAMDA’s inaugural conference – held in May 2023 – and its seminar series, as well as work performed by members of the Center. They showcase the interdisciplinary nature of data science, emphasizing its mathematical and theoretical foundations, especially those rooted in approximation theory. |
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Faster (2010 film) - Wikipedia
Faster is a 2010 American action thriller film directed by George Tillman Jr. [6] The film stars Dwayne Johnson, Billy Bob Thornton, …
Faster (2010) - IMDb
Faster: Directed by George Tillman Jr.. With Dwayne Johnson, Mauricio Lopez, Jim Gaines, Tom Berenger. An ex-con gets on a series …
Watch Faster | Prime Video - amazon.com
Faster Action star Dwayne Johnson stars as Driver, now a free man after a decade in prison, focused on hunting down the …
Faster - Official Trailer - YouTube
After 10 years in prison, Driver (Dwayne Johnson) has a singular focus - to avenge the murder of his brother during the botched …
Faster streaming: where to watch movie online? - JustWatch
Currently you are able to watch "Faster" streaming on Paramount+ Amazon Channel. It is also possible to buy "Faster" on …
