We analyze the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-onsolid model of statistical physics. This model has been proposed...
We show how to compute the edit distance between two strings of length n up to a factor of 2 ~O( log n) in n1+o(1) time. This is the first sub-polynomial approximation algorithm f...
We propose a fully homomorphic encryption scheme – i.e., a scheme that allows one to evaluate circuits over encrypted data without being able to decrypt. Our solution comes in t...
We give explicit constructions of epsilon nets for linear threshold functions on the binary cube and on the unit sphere. The size of the constructed nets is polynomial in the dime...
The discrete logarithm problem asks to solve for the exponent x, given the generator g of a cyclic group G and an element h ∈ G such that gx = h. We give the first rigorous pro...