We give a randomized 2 n+o(n) -time and space algorithm for solving the Shortest Vector
Problem (SVP) on n-dimensional Euclidean lattices. This improves on the previous fastest …

We give a 2 n+o(n) -time and space randomized algorithm for solving the exact Closest Vector
Problem (CVP) on n-dimensional Euclidean lattices. This improves on the previous fastest …

We consider the problem of finding a low discrepancy coloring for sparse set systems where
each element lies in at most $t$ sets. We give an efficient algorithm that finds a coloring with …

Explaining the excellent practical performance of the simplex method for linear programming
has been a major topic of research for over 50 years. One of the most successful …

In Rothvoß (Math Program 142(1–2):255–268, 2013 ) it was shown that there exists a 0/1
polytope (a polytope whose vertices are in $$\{0,1\}^{n}$$ { 0 , 1 } n ) such that any higher-…

We give a novel algorithm for enumerating lattice points in any convex body, and give
applications to several classic lattice problems, including the Shortest and Closest Vector …

An important result in discrepancy due to Banaszczyk states that for any set of n vectors in ℝ
m of ℓ 2 norm at most 1 and any convex body K in ℝ m of Gaussian measure at least half, …

We present a new efficient algorithm for the search version of the approximate Closest Vector
Problem with Preprocessing (CVPP). Our algorithm achieves an approximation factor of O(…

The frame scaling problem is: given vectors , marginals , and precision ɛ > 0, find left and
right scalings such that (v 1 ,…,v n ) := (Lu 1 r 1 ,…, Lu n r n ) simultaneously satisfies and , up …

We consider the task of proving integer infeasibility of a bounded convex $K$ in $\mathbb{R}^n$
using a general branching proof system. In a general branching proof, one constructs a …