Shubhangi Saraf, Ilya Volkovich
We study the problem of identity testing for multilinear ΣΠΣΠ(k) circuits, i.e. multilinear depth-4 circuits with fan-in k at the top + gate. We give the first polynomial-time deterministic identity testing algorithm for such circuits. Our ...
An argument system for NP is succinct, if its communication complexity is polylogarithmic the instance and witness sizes. The seminal works of Kilian '92 and Micali '94 show that such arguments can be constructed under standard cryptographic hardness ...
Let C be a depth-3 circuit with n variables, degree d and top fanin k (called ΣΠΣ(k,d,n) circuits) over base field FF. It is a major open problem to design a deterministic polynomial time blackbox algorithm that tests if C is identically zero. ...
Anupam Gupta, Moritz Hardt, Aaron Roth, Jonathan Ullman
Suppose we would like to know all answers to a set of statistical queries C on a data set up to small error, but we can only access the data itself using statistical queries. A trivial solution is to exhaustively ask all queries in C. Can we do any ...
Paul Christiano, Jonathan A. Kelner, Aleksander Madry, Daniel A. Spielman, Shang-Hua Teng
We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a system of ...
Shaddin Dughmi, Tim Roughgarden, Qiqi Yan
We design an expected polynomial time, truthful in expectation, (1-1/e)-approximation mechanism for welfare maximization in a fundamental class of combinatorial auctions. Our results apply to bidders with valuations that are matroid rank sums (MRS), ...
We show that every universally truthful randomized mechanism for combinatorial auctions with submodular valuations that provides an approximation ratio of m1/ 2 -ε must use exponentially many value queries, where m is the number of items. In ...
Atish Das Sarma, Stephan Holzer, Liah Kor, Amos Korman, Danupon Nanongkai, Gopal Pandurangan, David Peleg, Roger Wattenhofer
We study the verification problem in distributed networks, stated as follows. Let H be a subgraph of a network G where each vertex of G knows which edges incident on it are in H. We would like to verify whether H has some properties, e.g., if it is a ...
Christos H. Papadimitriou, George Pierrakos
We revisit the problem of designing the profit-maximizing single-item auction, solved by Myerson in his seminal paper for the case in which bidder valuations are independently distributed. We focus on general joint distributions, seeking the optimal ...
Shahar Dobzinski, Hu Fu, Robert D. Kleinberg
We consider the problem of designing a revenue-maximizing auction for a single item, when the values of the bidders are drawn from a correlated distribution. We observe that there exists an algorithm that finds the optimal randomized mechanism that ...