In this paper we consider the problem of constructing a small arithmetic circuit for a polynomial for which we have oracle access. Our focus is on n-variate polynomials, over a fi...
The degree of a polynomial representing (or approximating) a function f is a lower bound for the quantum query complexity of f. This observation has been a source of many lower bo...
Let g(n, r) be the maximum possible cardinality of a family F of subsets of {1, 2, . . . , n} so that given a union of at most r members of F, one can identify at least one of the...
We present a unified framework for reasoning about worst-case regret bounds for learning algorithms. This framework is based on the theory of duality of convex functions. It brin...
In the b-degree constrained Euclidean minimum spanning tree problem (bMST) we are given n points in [0;1]d and a degree constraint b 2. The aim is to nd a minimum weight spannin...