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

For any $\epsilon>0$, Laue and Matijevi\'{c} [CCCG'07, IPL'08] give a PTASfor finding a $(1+\epsilon)$-approximate solution to the $k$-hop MST problem inthe Euclidean plane that runs in time $(n/\epsilon)^{O(k/\epsilon)}$. In thispaper, we present an algorithm that runs in time $(n/\epsilon)^{O(\log k\cdot(1/\epsilon)^2\cdot\log^2(1/\epsilon))}$. This gives an improvement on thedependency on $k$ on the exponent, while having a worse dependency on$\epsilon$. As in Laue and Matijevi\'{c}, we follow the framework introduced byArora for Euclidean TSP. Our key ingredients include exponential distancescaling and compression of dynamic programming state tables.

A PTAS for $k$-hop MST on the Euclidean plane: Improving Dependency on $k$