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

We present an algorithm for evaluating a linear ``intersection transform'' ofa function defined on the lattice of subsets of an $n$-element set. Inparticular, the algorithm constructs an arithmetic circuit for evaluating thetransform in ``down-closure time'' relative to the support of the function andthe evaluation domain. As an application, we develop an algorithm that, givenas input a digraph with $n$ vertices and bounded integer weights at the edges,counts paths by weight and given length $0\leq\ell\leq n-1$ in time$O^*(\exp(n\cdot H(\ell/(2n))))$, where $H(p)=-p\log p-(1-p)\log(1-p)$, and thenotation $O^*(\cdot)$ suppresses a factor polynomial in $n$.

The fast intersection transform with applications to counting paths