PPT-Area Approximation

4B Exact Area Use geometric shapes such as rectangles circles trapezoids triangles etc rectangle triangle parallelogram Approximate Area Midpoint. . of Edit Distance. Robert Krauthgamer, . Weizmann Institute of Science. SPIRE 2013. TexPoint. fonts used in EMF. . Read the . TexPoint. manual before you delete this box. .: . A. A. A. A. A. A. A. Differentials and Linear Approximation. BC Calculus. Related Rates :. How . fast . is . y . changing as . x . is changing?. -. Differentials:. How . much. does . y . change as . x . changes?. area A 2 A = 212 r Proof___________In the figure below, observe that 21 a It is also evident from the green sin (2)Therefore, upon substituting from into Area 21a b sin ( * ) 8 2 A = 1. Tsvi. . Kopelowitz. Knapsack. Given: a set S of n objects with weights and values, and a weight bound:. w. 1. , w. 2. , …, w. n. , B (weights, weight bound).. v. 1. , v. 2. , …, v. n. (values - profit).. Actual area under curve:. Left-hand rectangular approximation:. Approximate area:. (too low). Approximate area:. Right-hand rectangular approximation:. (too high). Averaging the two:. 1.25% error. (too high). Sometimes we can handle NP problems with polynomial time algorithms which are guaranteed to return a solution within some specific bound of the optimal solution. within a constant . c. . of the optimal. Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. C-approximation. Optimization problem: output has a value that we want to . maximize . or . minimize. An algorithm A is an . Problem. Yan Lu. 2011-04-26. Klaus Jansen SODA 2009. CPSC669 Term Project—Paper Reading. 1. Problem Definition. 2. Approximation Scheme. 2.1 Instances with similar capacities. 2.2 General cases . Outline. δ. -Timeliness. Carole . Delporte-Gallet. , . LIAFA . UMR 7089. , Paris VII. Stéphane Devismes. , VERIMAG UMR 5104, Grenoble I. Hugues Fauconnier. , . LIAFA . UMR 7089. , Paris VII. LIAFA. Motivation. STATISTICS. Friday. March 7. Go over assignments. (Fri) A#6.32 . pg. . 267 #1-3 all, 16-26 even, 29, 30. (Mon) A#6.33A p . 267 #4, 35-38 all . Notes . – Section . 6.4 . . . Normal Approximation to the Binomial Distribution. How accurate is your estimate?. Differential Notation. The Linear Approximation to . y. = . f. (. x. ) is often written using the “differentials” . dx. and . dy. . In this notation, . dx. is used instead of . Chapter 5.5. Linear Approximation. A useful characteristic of the tangent line to a curve at a point is that, for . -values near the point, the curve is approximately linear. In fact, the function values of the curve are approximated by the derivative values near the point of tangency. Stochastic . Optimization. Anupam Gupta. Carnegie Mellon University. IPCO Summer . School. Approximation . Algorithms for. Multi-Stage Stochastic Optimization. {vertex cover, . S. teiner tree, MSTs}. When the best just isn’t possible. Jeff Chastine. Approximation Algorithms. Some NP-Complete problems are too important to ignore. Approaches:. If input small, run it anyway. Consider special cases that may run in polynomial time.