PPT-Bounded Approximation Algorithms

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. . 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. Ravishankar. . Krishnaswamy. (joint work with Nikhil . Bansal. and . Barna. . Saha. ). Approximating Set Cover. Given . m sets, n elements. Find . minimum cost. collection of sets . to cover . Daniel . Dadush (CWI). Joint . with Santosh . Vempala. Volume Estimation. Given convex body . and factor . , compute . such that . ..  .  . given by a membership oracle..  .  .  . Volume Estimation. 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).. Yuri Gurevich. SOFSEM 2012. 1. The Czech . connection of “Gurevich”. z . Hořovice. . . von Horowitz .  Horowitz . Horowicz. , . Hurwicz. . Гуреви. ч . . Gurevich. 2. Agenda. Lecture 12. Constantinos Daskalakis. The Lemke-. Howson. Algorithm. The Lemke-. Howson. Algorithm (1964). Problem:. Find an exact equilibrium of a 2-player game.. Since there exists a rational equilibrium this task is feasible.. 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 . Algorithms. and Networks 2015/2016. Hans L. . Bodlaender. Johan M. M. van Rooij. TexPoint fonts used in EMF. . Read the TexPoint manual before you delete this box.: . A. A. A. A. A. A. A. A. A. A. What to do if a problem is. 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. 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 . Daniel . Dadush (CWI). Joint . with Santosh . Vempala. Volume Estimation. Given convex body . and factor . , compute . such that . ..  .  . given by a membership oracle..  .  .  . Volume Estimation. How do weights affects approximation algorithms?. As usual there are no rules whatsoever.. However I will provide some interesting examples in which weights make a difference. I will try and say for every problem, why weights make a difference.. Pravesh Kothari, . Divyarthi Mohan,. Ariel Schvartzman, . Sahil Singla, S. Matthew Weinberg. FOCS 2019. How to Maximize Revenue?. Selling a Single Item. ~ .  . v(. ⚽. ). v(. ⚽. )= . x. Truthful Mechanism.