English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We give a deterministic O(log n)^n algorithm for the {\em Shortest VectorProblem (SVP)} of a lattice under {\em any} norm, improving on the previousbest deterministic bound of n^O(n) for general norms and nearly matching thebound of 2^O(n) for the standard Euclidean norm established by Micciancio andVoulgaris (STOC 2010). Our algorithm can be viewed as a derandomization of theAKS randomized sieve algorithm, which can be used to solve SVP for any norm in2^O(n) time with high probability. We use the technique of covering a convexbody by ellipsoids, as introduced for lattice problems in (Dadush et al., FOCS2011).  Our main contribution is a deterministic approximation of an M-ellipsoid ofany convex body. We achieve this via a convex programming formulation of theoptimal ellipsoid with the objective function being an n-dimensional integralthat we show can be approximated deterministically, a technique that appears tobe of independent interest.

Deterministic Construction of an Approximate M-Ellipsoid and its Application to Derandomizing Lattice Algorithms