Near-Optimal Deterministic Algorithms for Volume Computation and Lattice Problems via M-Ellipsoids
نویسندگان
چکیده
We give a deterministic 2 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 for the shortest and closest lattice vector problems under general norms.
منابع مشابه
Near-optimal deterministic algorithms for volume computation via M-ellipsoids
This bound is achieved by the maximum volume ellipsoid contained in K. Ellipsoids have also been critical to the design and analysis of efficient algorithms. The most notable example is the ellipsoid algorithm (1, 2) for linear (3) and convex optimization (4), which represents a frontier of polynomial-time solvability. For the basic problems of sampling and integration in high dimension, the in...
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