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

Given a graph, the sparsest cut problem asks for a subset of vertices whoseedge expansion (the normalized cut given by the subset) is minimized. In thispaper, we study a generalization of this problem seeking for $ k $ disjointsubsets of vertices (clusters) whose all edge expansions are small andfurthermore, the number of vertices remained in the exterior of the subsets(outliers) is also small. We prove that although this problem is $ NP-$hard fortrees, it can be solved in polynomial time for all weighted trees, providedthat we restrict the search space to subsets which induce connected subgraphs.The proposed algorithm is based on dynamic programming and runs in the worstcase in $ O(k^2 n^3) $, when $ n $ is the number of vertices and $ k $ is thenumber of clusters. It also runs in linear time when the number of clusters andthe number of outliers is bounded by a constant.

Multi-way sparsest cut problem on trees with a control on the number of parts and outliers