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 dataset of points in a metric space and an integer $k$, a diversitymaximization problem requires determining a subset of $k$ points maximizingsome diversity objective measure, e.g., the minimum or the average distancebetween two points in the subset. Diversity maximization is computationallyhard, hence only approximate solutions can be hoped for. Although itsapplications are mainly in massive data analysis, most of the past research ondiversity maximization focused on the sequential setting. In this work wepresent space and pass/round-efficient diversity maximization algorithms forthe Streaming and MapReduce models and analyze their approximation guaranteesfor the relevant class of metric spaces of bounded doubling dimension. Likeother approaches in the literature, our algorithms rely on the determination ofhigh-quality core-sets, i.e., (much) smaller subsets of the input which containgood approximations to the optimal solution for the whole input. For a varietyof diversity objective functions, our algorithms attain an$(\alpha+\epsilon)$-approximation ratio, for any constant $\epsilon>0$, where$\alpha$ is the best approximation ratio achieved by a polynomial-time,linear-space sequential algorithm for the same diversity objective. Thisimproves substantially over the approximation ratios attainable in Streamingand MapReduce by state-of-the-art algorithms for general metric spaces. Weprovide extensive experimental evidence of the effectiveness of our algorithmson both real world and synthetic datasets, scaling up to over a billion points.

MapReduce and Streaming Algorithms for Diversity Maximization in Metric Spaces of Bounded Doubling Dimension