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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

To find the number of assignments of zeros and ones satisfying a specificKnapsack Problem is $\#P$ hard, so only approximations are envisageable. AMarkov chain allowing uniform sampling of all possible solutions is given byLuby, Randall and Sinclair. In 2005, Morris and Sinclair, by using a flowargument, have shown that the mixing time of this Markov chain is$\mathcal{O}(n^{9/2+\epsilon})$, for any $\epsilon > 0$. By using a canonicalpath argument on the distributive lattice structure of the set of solutions, weobtain an improved bound, the mixing time is given as $\tau_{_{x}}(\epsilon)\leq n^{3} \ln (16 \epsilon^{-1})$.

Mixing Time of Markov chain of the Knapsack Problem