Near-Optimal Deterministic Algorithms for Volume Computation and Lattice   Problems via M-Ellipsoids
  We give a deterministic 2^{O(n)} algorithm for computing an M-ellipsoid of a convex body, matching a known lower bound. This has several interesting consequences including improved deterministic algorithms for volume estimation of convex bodies and the shortest and closest lattice vector problems under general norms. 
Daniel Dadush and Santosh Vempala
cs.CC cs.DS math.FA