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. Robust Approximation Bounds for . Equilibria. and Auctions. Tim . Roughgarden. Stanford University. 2. Motivation. Clearly: . many modern applications in CS involve autonomous, self-interested agents. 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 . 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. 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).. 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 . unseen problems. David . Corne. , Alan Reynolds. My wonderful new algorithm, . Bee-inspired Orthogonal Local Linear Optimal . Covariance . K. inetics . Solver. Beats CMA-ES on 7 out of 10 test problems !!. approximate membership. dynamic data structures. Shachar. Lovett. IAS. Ely . Porat. Bar-. Ilan. University. Synergies in lower bounds, June 2011. Information theoretic lower bounds. Information theory. Grigory. . Yaroslavtsev. http://grigory.us. . With . Shuchi. . Chawla. (University of Wisconsin, Madison),. Konstantin . Makarychev. (Microsoft Research),. Tselil. Schramm (University of California, Berkeley). Daniel . Dadush (CWI). Joint . with Santosh . Vempala. Volume Estimation. Given convex body . and factor . , compute . such that . ..  .  . given by a membership oracle..  .  .  . Volume Estimation. A PRIORI BOUNDS ON THE PERFORMANCE OFOPTIMAL SYSTEMSbyROBERTO CANALES RUIZIE Universidad de los Andes1963BS Massachusetts Institute of Technology1963MS Massachusetts Institute of Technology1965SUBMITT 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. 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.