2008-2009 Seminars

A halfspace (a.k.a. threshold) is a boolean function h : {-1,1}^n --> {-1,1} of the form h(x) = sign(w_0 + w_1 x_1 + ... + w_n x_n), where the weights w_i are arbitrary real numbers. Halfspaces are studied extensively in the theories of complexity...

The Parallel Repetition Theorem by Raz is used to amplify the soundness of PCP's, and is one of the ingredients to prove strong inapproximability results. Unfortunately, Raz's proof was very complicated. In these two talks, I will present the...

This work attempts to broaden the foundations of public-key cryptography. We construct a new public key encryption based on two “hardness on average” assumptions: (1) it is hard to “learn parity with noise” for random sparse equations; and (2) it is...

Does computing n copies of a function require n times the computational effort? In this work, we give the first non-trivial answer to this question for the model of randomized communication complexity. We show that: 1. Computing n copies of a...

A number of recent results on optimization problems involving submodular functions have made use of the "multilinear relaxation" of the problem. I will show a general approach to deriving inapproximability results in the value oracle model, based on...

The local ratio framework introduced by Bar Yehuda and Evan in 1981 provides a unified framework for many approximation algorithms. Recently, the local ratio technique has been used to provide efficient approximation algorithms for a number of...