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

The \emph{maximal $k$-edge-connected subgraphs} problem is a classical graphclustering problem studied since the 70's. Surprisingly, no non-trivialtechnique for this problem in weighted graphs is known: a very straightforwardrecursive-mincut algorithm with $\Omega(mn)$ time has remained the fastestalgorithm until now. All previous progress gives a speed-up only when the graphis unweighted, and $k$ is small enough (e.g.~Henzinger~et~al.~(ICALP'15),Chechik~et~al.~(SODA'17), and Forster~et~al.~(SODA'20)).  We give the first algorithm that breaks through the long-standing$\tilde{O}(mn)$-time barrier in \emph{weighted undirected} graphs. Morespecifically, we show a maximal $k$-edge-connected subgraphs algorithm thattakes only $\tilde{O}(m\cdot\min\{m^{3/4},n^{4/5}\})$ time. As an immediateapplication, we can $(1+\epsilon)$-approximate the \emph{strength} of all edgesin undirected graphs in the same running time.  Our key technique is the first local cut algorithm with \emph{exact}cut-value guarantees whose running time depends only on the output size. Allprevious local cut algorithms either have running time depending on the cutvalue of the output, which can be arbitrarily slow in weighted graphs or haveapproximate cut guarantees.

Maximal $k$-Edge-Connected Subgraphs in Weighted Graphs via Local Random Contraction