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| | Approximation - Wikipedia, the free encyclopedia |
 | | The type of approximation used depends on the available information, the degree of accuracy required, the sensitivity of the problem to this data, and the savings (usually in time and effort) that can be achieved by approximation. | | | Approximations may be used because incomplete information prevents use of exact representations. | | | An approximation is an inexact representation of something that is still close enough to be useful. |
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http://en.wikipedia.org/wiki/Approximation
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| | Approximation Methods Panel |
| | Approximation methods are becoming popular tools for modeling uncertainty and reducing the computational expense of probabilistic analysis during probabilistic design optimization. | | | He stated that approximation methods are finding new uses in reducing the computational expensive of probabilistic analysis to make probabilistic optimization more tractable. | | | Once the approximation model is constructed, it must be validated in order to ensure that it is sufficiently accurate to use as a surrogate for the original code. |
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http://www.me.psu.edu/simpson/approximation/approx-panel.html
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| | 550.770 Approximation Algorithms |
| | Trading-off optimality in favor of tractibility is the paradigm of approximation algorithms. | | | Approximation algorithms have developed in response to the impossibility of solving a good many problems exactly. | | | In the case of NP-Complete problems, we sacrifice optimality in favor of a ``good'' solution that can be computed efficiently. |
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http://www.cs.jhu.edu/%7Ecowen/approx.html
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| | The Normal Approximation to the Binomial |
| | Exercise #1 computes binomial probabilities and quantiles for the distribution of girl births and compares them to probabilities computed approximately using a normal approximation. | | | Example #1 computes binomial probabilities and quantiles for the distribution of hotel room occupancies and compares them to probabilities computed approximately using a normal approximation. | | | can be used to experiment with computing approximate and exact binomial probabilities and to assess the conditions for which the normal approximation to the binomial distribution is good. |
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http://www.stat.wvu.edu/SRS/Modules/NormalApprox/normalapprox.html
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| | Approximation Algorithms |
| | Approximation Algorithms for Covering with Fixed Size Hypersquares and Related Problems, Proceedings of the 29th Annual Allerton Conference on Communications, Control and Computing, October 1990, pp. | | | Complexity and Approximations for Multimessage Multicasting, Journal of Parallel and Distributed Computing, 55, 1998, 215 -- 235. | | | An Approximation Algorithm for Partitioning a Hyperrectilinear Polygon with Holes, (with M. Razzazi), UCSB Technical Report TRCS 90--23, November, 1990. |
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http://www.cs.ucsb.edu/~teo/publications/APROX.html
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| | Eva Tardos, Department of Computer Science, Cornell University |
| | A Constant Factor Approximation Algorithm for a Class of Classification Problems, In the Proceedings of the ACM Symposium on the Theory of Computing, May 2000. | | | My research is concerned with the design and analysis of algorithms for fundamental problems in network, combinatorial optimization, approximation algorithms, on-line algorithms, linear and integer programming, and their applications to various problems. | | | A constant-factor approximation algorithm for the k-median problem. |
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http://www.cs.cornell.edu/People/eva/eva.html
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| | Approximation Algorithms |
| | 236521 is a course on approximation algorithms for NP-hard combinatorial optimization problems given for the second year at the Technion's Computer Science Department. | | | It is suitable as a high-level undergraduate course, and as a graduate course. | | | Lecture 13: MAX-SNP and hardness of approximation results; concluding remarks, open problems. |
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http://www.cs.technion.ac.il/~rabani/236521.95.wi.html
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| | Approximation algorithm - Education - Information - Educational Resources - Encyclopedia - Music |
| | In computer science, approximation algorithms are an approach to attacking NP-hard optimization problems. | | | Another limitation of the approach is that it applies only to optimization problems and not to “pure” decision problems like Satisfiability. | | | A typical example for an approximation algorithm is the one for vertex cover: Find an uncovered edge and take both end points into the vertex cover. |
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http://www.music.us/education/A/Approximation-algorithm.htm
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| | David <<<<b>bb>>bb>bb>>><b>bb>b>bb>>bb>bb>>>><<b>bb>>Bb>bb>>b>bb>>bb>bb>>><b>bb>b>bb>>bb>bb>>>>. Shmoys |
| | The primary focus of my research is on the design and analysis of efficient algorithms for discrete optimization problems, and in particular, on approximation algorithms for NP-hard and other computationally intractable problems. | | | Analogously, from a theoretical perspective, for some NP-hard optimization problems it is possible to efficiently compute solutions that are guaranteed to be arbitrarily close to optimal, whereas for others, computing even a crude approximation to the optimum is also NP-hard. | | | Since the primary means of solving these problems (to optimality) also involves the solution of a sequence of such relaxations, this algorithmic approach dovetails well with the foremost technology for proving optimality, and hence has substantial potential for improving these optimization techniques as well. |
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http://www.orie.cornell.edu/%7Eshmoys
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| | Approximation Algorithms(Part I of II) |
| | The approximation algorithms approach is particularly suitable for use in the context of integer programming algorithms because the analysis provides a feasible approximate solution as well as a "bound" that leads to an estimate on the gap between the optimal and the feasible solutions. | | | Approximation algorithms have emerged as a major tool for coping with intractability of problems. | | | There are current efforts to unify the ad hoc techniques that have been used for approximation algorithms. |
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http://www.siam.org/meetings/dm98/ms18.htm
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| | Backprop Learning Tool |
| | In each case, the dotted line is the underlying function to be approximated, the solid line is the neural net output, and the open circles indicate the data points used for training. | | | The reason for this phenomenon is that the network "overfits" the data, i.e., the network tries to fit the noise in the data as well as the underlying function to be approximated. | | | Note that no attempt has been made to optimize the network size or the value of the learning rates. |
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http://neuron.eng.wayne.edu/bpFunctionApprox/bpFunctionApprox.html
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| | Neural Networks for Optimal Approximation of Smooth and Analytic Functions - Mhaskar (ResearchIndex) |
| | We prove that neural networks with a single hidden layer are capable of providing an optimal order of approximation for functions assumed to possess a given number of derivatives, if the activation function evaluated by each principal element satisfies certain technical conditions. | | | 211 Universal approximation bounds for superposition of a sigmoi.. | | | 12 Approximation by superposition of a sigmoidal function and r.. |
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http://citeseer.ist.psu.edu/mhaskar96neural.html
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| | David <<<<b>bb>>bb>bb>>><b>bb>b>bb>>bb>bb>>>><<b>bb>>Bb>bb>>b>bb>>bb>bb>>><b>bb>b>bb>>bb>bb>>>>. Shmoys: Selected Recent Publications |
| | In: Approximation Algorithms for Combinatorial Optimization, Lecture Notes in Computer Science 1444 (K. Jansen and J. Rolim, eds.), Springer, Berlin, 1998, 15-32. | | | In: Approximation Algorithms for Combinatorial Optimization, Lecture Notes in Computer Science 1913, (K. Jansen and S. Khuller, eds.), Springer, Berlin, 2000, 27-33. | | | "Sampling-based approximation algorithms for multi-stage stochastic optimization.".ps version To appear in FOCS 2005. |
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http://www.orie.cornell.edu/%7Eshmoys/publications.html
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| | Approximation Algorithms |
| | Approximation Algorithms for Bin Packing: A Survey, E. Coffman, Jr., M. Garey, and D. Johnson, Approximation Algorithms for NP-Hard Problems, D. Hochbaum (editor), PWS Publishing, Boston (1997), 46-93. | | | A chapter on the book "Approximation Algorithms for NP hard optimization problems". | | | Approximability of Optimization Problems, MIT, Fall 99 (Lecturer: Madhu Sudan) |
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http://www.csd.uwo.ca/~bma/teaching/approx/resources.html
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| | AFSJ - The approximation of European law |
| | The two processes must be conducted jointly but also autonomously, because mutual recognition and approximation pursue two different objectives. | | | They have so far addressed this question only on a case-by-case basis, approximating not the maximum sentences themselves, but only minimum levels for maximum sentences. | | | The approximation of offences related to corruption in the public sector is addressed in a Protocol to the Convention on the protection of the Communities’ financial interests adopted on 27 September 1996 and in a Convention adopted on 26 May 1997. |
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http://www.europarl.eu.int/comparl/libe/elsj/zoom_in/20_en.htm
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| | waoa03.html |
| | Approximation and online algorithms are fundamental tools used to deal with computationally hard problems and problems in which the input is gradually disclosed over time. | | | The proceedings of the workshop will be published as a volume in either the series Lecture Notes in Computer Science or Electronic Notes in Theoretical Computer Science. | | | An ARACNE mini-symposium on approximation and randomized algorithms in communication networks will take place as part of the workshop. |
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http://www.informatik.uni-kiel.de/inf/Jansen/conference/waoa03.html
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| | pubs.html |
| | Approximation Algorithms for the Largest Common Subtree Problem. | | | Approximation Algorithms for the Metric Labeling Problem via a New Linear Programming Formulation. | | | Approximation Algorithms for Data Placement on Parallel Disks. |
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http://www.cis.upenn.edu/%7Esanjeev/pubs.html
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| | PCP Links |
| | A survey of approximation algorithms for combinatorial optimization problems. | | | Indicates, for each problem, both the factor achieved by the best known approximation algorithm and the best known hardness result, with references to the relevant sources. | | | A comprehensive summary of the current approximability status of over 150 optimization problems. |
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http://www-cse.ucsd.edu/users/mihir/pcp.html
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| | A 5/8 Approximation Algorithm for the Maximum Asymmetric TSP |
| | We propose a polynomial time approximation algorithm for the problem with a 5/8 approximation guarantee. | | | A 5/8 Approximation Algorithm for the Maximum Asymmetric TSP: SIAM Journal on Discrete Mathematics Vol. | | | This (1) improves upon the approximation factors of previous results and (2) presents a simpler solution to the previously fairly involved algorithms. |
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http://epubs.siam.org/sam-bin/dbq/article/40286
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| | Amazon.com: Books: Approximation Algorithms |
| | Richard Karp,University Professor, University of California at Berkeley Following the development of basic combinatorial optimization techniques in the 1960s and 1970s, a main open question was to develop a theory of approximation algorithms. | | | Approximation Algorithms for NP-Hard Problems by Pws Pub Co | | | This book covers the dominant theoretical approaches to the approximate solution of hard combinatorial optimization and enumeration problems. |
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http://www.amazon.com/exec/obidos/tg/detail/-/3540653678?v=glance
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| | A More Efficient Approximation Scheme for Tree Alignment |
| | As in the existing PTASs in the literature, the basic approach of our algorithm is to partition the given tree into overlapping components of a constant size and then apply local optimization on each such component. | | | Moreover, the performance of the PTAS is more sensitive to the size of the components, which basically determines the running time, and we obtain an improved approximation ratio for each size. | | | A More Efficient Approximation Scheme for Tree Alignment: SIAM Journal on Computing Vol. |
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http://epubs.siam.org/sam-bin/dbq/article/31350
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| | Amazon.com: Books: Approximation Algorithms for NP-Hard Problems |
| | Developing approximation algorithms for NP hard problems is now a very active field in Mathematical Programming and Theoretical Computer Science. | | | Provides computer scientists and operations researchers with an effective framework for analyzing approximation algorithms and applying them to the solution of intractable problems. | | | With chapters contributed by leading researchers in the field, this book introduces unifying techniques in the analysis of approximation algorithms. |
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http://www.amazon.com/exec/obidos/tg/detail/-/0534949681?v=glance
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| | 6.893: Approximability of Optimization Problems |
| | Preliminary version of a book on Approximation Algorithms by Rajeev Motwani, 1992. | | | Lecture 1 (9/8): Introduction to NP, NP Optimization, Approximation. | | | For now here are some sources for approximation algorithms; and hardness of approximations. |
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http://theory.lcs.mit.edu/~madhu/FT99/course.html
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| | Rational Approximation Experiments |
| | Altho this formal transformation cannot add any information to the approximation, experimentally it appears that, for many functions, the Pade transformation of the Taylor or Chebyshev approximation is better than the original approximation. | | | Alternatively, it's possible that rational approximations are defective, and do not exist for many degrees. | | | Since the distribution of the error can also be interesting, for most methods, I will also plot the error between arcsin and the approximating function. |
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http://www.ecse.rpi.edu/Homepages/wrf/Research/Short_Notes/arcsin
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| | Definition of Approximation |
| | Though our result is discouraging, we recall that the infinite limits approximation may in fact be simulated by using a different windowing function, as has been covered earlier. | | | To explore the validity of the infinite limits approximation for the rectangle window case, we will compare this approximation to that made above (the large limits approximation). | | | Here, we consider why this is not valid for the rectangle window case. |
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http://ccrma-www.stanford.edu/~asmaster/fresnelanalpaper/fresnelanal/node56.html
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| | APPROX 2002 Home Page |
| | The workshop on approximation algorithms for combinatorial optimization problems focuses on algorithmic and complexity aspects arising in the development of efficient approximate solutions to computationally difficult problems. | | | APPROX 2001, 4th International Workshop on Approximation Algorithms for Combinatorial Optimization, Berkeley, CA, USA, 2001. | | | International Workshop on Approximation Algorithms for Combinatorial Optimization |
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http://www.dis.uniroma1.it/~algo02/approx02
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| | Learning and Value Function Approximation in Complex Decision Processes |
| | Unfortunately, exact computation of the value function typically requires time and storage that grow proportionately with the number of states, and consequently, the enormous state spaces that arise in practical applications render the algorithms intractable. | | | We also present a computational case study involving a complex optimal stopping problem that is representative of those arising in the financial derivatives industry. | | | As a special case of temporal--difference learning in a context involving control, we propose variants of the algorithm that generate approximate solutions to optimal stopping problems. |
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http://web.cps.msu.edu/rlr/pub/VanRoy1.html
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| | Approximation Algorithms for NP-Hard Problems |
| | The approximation algorithms' framework provides a guarantee on the quality of the solution obtained. | | | Such problems are commonly addressed with heuristics that provide a solution, but not information on the solution's quality. | | | This framework has been used as a guide to developing algorithms in specific problem areas with increasingly improved performance. |
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http://www.ieor.berkeley.edu/~hochbaum/html/book-aanp.html
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| | Approximation |
| | If you estimate the position of the object by neglecting changes in velocity, then the result is a Linear Approximation to the true position function, and its graph is just the tangent line to the true graph. | | | The Differential and Tangent Line Approximations can be used to estimate experimental errors and to get approximate results for calculations that would be hard to do exactly. | | | (This should work because there are three conditions to match and a quadratic has three coefficients for us to choose.) And for even better approximations we might match higher derivatives by using higher degree polynomials. |
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http://www.langara.bc.ca/mathstats/resource/onWeb/calculus/approximation
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