A novel algorithm for enumerating lattice points in any convex body known as the M-ellipsoid is given, and an expected O(f*(n))^n-time algorithm for Integer Programming, where f*( n) denotes the optimal bound in the so-calledflatnesstheorem, which is conjectured to be f* (n) = O(n).Expand

A new 2O(n) nn time algorithm is given, which yields the fastest currently known algorithm for IP and improves on the classic works of Lenstra and Kannan, to give a new and tighter proof of the atness theorem.Expand

This paper gives an efficient randomized algorithm to find a ± 1 combination of the vectors which lies in cK for c>0 an absolute constant, which leads to new efficient algorithms for several problems in discrepancy theory.Expand

The SVP result follows from a natural reduction from SVP to DGS, and a more refined algorithm for DGS above the so-called smoothing parameter of the lattice, which can generate 2n/2 discrete Gaussian samples in just 1.93-approximate decision SVP.Expand

A substantially more efficient variant of the LLM algorithm is presented, and via an improved analysis, it is shown that it can decode up to a distance proportional to the reciprocal of the smoothing parameter of the dual lattice.Expand

An efficient algorithm is given that finds a coloring with discrepancy O((t log n)1/2), matching the best known non-constructive bound for the problem due to Banaszczyk, and gives an algorithmic O(log 1/2 n) bound.Expand

The degenerate case $\rho_A=0$ is addressed by extending the algorithms to find maximum support nonnegative vectors in the kernel of A and in the image of A^\top by extending them to the oracle setting.Expand

In this paper, we show that the Chvátal–Gomory closure of any compact convex set is a rational polytope. This resolves an open question of Schrijver (Ann Discret Math 9:291–296, 1980) for irrational… Expand

In this paper, we prove that the Chvatal-Gomory closure of a set obtained as an intersection of a strictly convex body and a rational polyhedron is a polyhedron. Thus, we generalize a result of… Expand