PPT-Approximation of

δ Timeliness Carole DelporteGallet LIAFA UMR 7089 Paris VII Stéphane Devismes VERIMAG UMR 5104 Grenoble I Hugues Fauconnier LIAFA UMR 7089 Paris VII LIAFA Motivation. Prasad . Raghavendra. . Ning. Chen C. . . Thach. . Nguyen . . . Atri. . Rudra. . . Gyanit. Singh. University of Washington. Roee . Engelberg. Technion. University. Ankush Sharma . A0079739H. Xiao Liu . A0060004E. Tarek Ben Youssef A0093229. Reference. Terminologies – TSP & PTAS (Polynomial Time Approximation Schemes). Algorithm – A PTAS for Euclidian TSP (2D). A Mini-Survey. Chandra . Chekuri. Univ. of Illinois, Urbana-Champaign. Submodular Set Functions. A function . f. : 2. N. . . . R . is submodular if. . f(A. ) + . f(B. ) ≥ . f(A. . B. ) + . 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 . Problems. Proofs. Approximations. Decision Problems. Given Some Universal Set X,. Let R be a subset of X.. The decision problem for R is:. Given an arbitrary element a of X, does. a belong to R?. Note: X is usually assumed to be a set of . Reuven. Bar-. Yehuda. . Gleb. . Polevoy. Dror. . Rawitz. . . Technion. 1. Multiple interference. 2. . w. e can . approximate. to . . For small interferences. Interval selection with multiple interference. A Mini-Survey. Chandra . Chekuri. Univ. of Illinois, Urbana-Champaign. Submodular Set Functions. A function . f. : 2. N. . . . R . is submodular if. . f(A. ) + . f(B. ) ≥ . f(A. . B. ) + . Julia Chuzhoy. Toyota Technological Institute at Chicago. Routing Problems. Input. : Graph G, source-sink pairs (s. 1. ,t. 1. ),…,(. s. k. ,t. k. ).. Goal. : Route as many pairs as possible; minimize edge congestion.. *University . of California . Berkeley. Mohsen Imani, . Abbas . Rahimi. *. , . Tajana S. Rosing. Resistive Configurable Associative Memory . for Approximate . Computing. Motivation. 2. Internet of Things. Grigory. . Yaroslavtsev. . Penn State + AT&T Labs - Research (intern). Joint work with . Berman (PSU). , . Bhattacharyya (MIT). , . Makarychev. (IBM). , . Raskhodnikova. (PSU). Directed. Spanner Problem. 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 .