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 show that a constant factor approximation of the shortest and closestlattice vector problem in any norm can be computed in time $2^{0.802\, n}$.This contrasts the corresponding $2^n$ time, (gap)-SETH based lower bounds forthese problems that even apply for small constant approximation. For bothproblems, $\mathrm{SVP}$ and $\mathrm{CVP}$, we reduce to the case of theEuclidean norm. A key technical ingredient in that reduction is a twist ofMilman's construction of an $M$-ellipsoid which approximates any symmetricconvex body $K$ with an ellipsoid $\mathcal{E}$ so that $2^{\varepsilon n}$translates of a constant scaling of $\mathcal{E}$ can cover $K$ and vice versa.

Approximate $\mathrm{CVP}$ in time $2^{0.802 \, n}$ -- now in any norm!