We consider the problem of determining whether a given set S in Rn is approximately convex, i.e., if there is a convex set K ∈ Rn such that the volume of their symmetric differe...
We give a deterministic O(log n)n -time and space algorithm for the Shortest Vector Problem (SVP) of a lattice under any norm, improving on the previous best deterministic nO(n) -...
Abstract. In this paper, we propose a Markov chain for sampling a random vector distributed according to a discretized Dirichlet distribution. We show that our Markov chain is rapi...
Abstract. We are interested in efficient algorithms for generating random samples from geometric objects such as Riemannian manifolds. As a step in this direction, we consider the ...
We consider optimization problems that can be formulated as minimizing the cost of a feasible solution wT x over an arbitrary combinatorial feasible set F {0, 1}n . For these pro...