PPT-Optimal bounds on approximation

of submodular and XOS functions by juntas Vitaly Feldman and Jan Vondrâk IBM Research Almaden Prelims Submodular and XOS Functions Learning 20 27 Approximation by juntas. Prasad . Raghavendra. . Ning. Chen C. . . Thach. . Nguyen . . . Atri. . Rudra. . . Gyanit. Singh. University of Washington. Roee . Engelberg. Technion. University. Shubhangi. . Saraf. Rutgers University. Based on joint works with . Albert Ai, . Zeev. . Dvir. , . Avi. . Wigderson. Sylvester-. Gallai. Theorem (1893). v. v. v. v. Suppose that every line through . Matt Weinberg. MIT .  Princeton  MSR. References: . . http. ://arxiv.org/abs/. 1305.4002. http. ://arxiv.org/abs/. 1405.5940. http. ://arxiv.org/abs/. 1305.4000. Recap. Costis. ’ Talk: . Optimal multi-dimensional mechanism: additive bidders, no constraints. Daniel . Dadush (CWI). Joint . with Santosh . Vempala. Volume Estimation. Given convex body . and factor . , compute . such that . ..  .  . given by a membership oracle..  .  .  . Volume Estimation. 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. 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 . Grigory. . Yaroslavtsev. http://grigory.us. . With . Shuchi. . Chawla. (University of Wisconsin, Madison),. Konstantin . Makarychev. (Microsoft Research),. Tselil. Schramm (University of California, Berkeley). Stochastic . Optimization. Anupam Gupta. Carnegie Mellon University. IPCO Summer . School. Approximation . Algorithms for. Multi-Stage Stochastic Optimization. {vertex cover, . S. teiner tree, MSTs}. EECT 7327 . Fall 2014. Successive Approximation. (SA) ADC. Successive Approximation ADC. – . 2. –. Data Converters Successive Approximation ADC Professor Y. Chiu. EECT 7327 . Fall 2014. Binary search algorithm → N*. 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. dynamic data structures. Shachar. Lovett. IAS. Ely . Porat. Bar-. Ilan. University. Synergies in lower bounds, June 2011. Information theoretic lower bounds. Information theory. is a powerful tool to prove lower bounds, e.g. in data structures. Dagstuhl Workshop. March/. 2023. Igor Carboni Oliveira. University of Warwick. 1. Join work with . Jiatu. Li (Tsinghua). 2. Context. Goals of . Complexity Theory. include . separating complexity classes.