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 propose an efficient algorithm for graph matching based on similarityscores constructed from counting a certain family of weighted trees rooted ateach vertex. For two Erd\H{o}s-R\'enyi graphs $\mathcal{G}(n,q)$ whose edgesare correlated through a latent vertex correspondence, we show that thisalgorithm correctly matches all but a vanishing fraction of the vertices withhigh probability, provided that $nq\to\infty$ and the edge correlationcoefficient $\rho$ satisfies $\rho^2>\alpha \approx 0.338$, where $\alpha$ isOtter's tree-counting constant. Moreover, this almost exact matching can bemade exact under an extra condition that is information-theoreticallynecessary. This is the first polynomial-time graph matching algorithm thatsucceeds at an explicit constant correlation and applies to both sparse anddense graphs. In comparison, previous methods either require $\rho=1-o(1)$ orare restricted to sparse graphs.  The crux of the algorithm is a carefully curated family of rooted treescalled chandeliers, which allows effective extraction of the graph correlationfrom the counts of the same tree while suppressing the undesirable correlationbetween those of different trees.

Random graph matching at Otter's threshold via counting chandeliers