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 consider the online $k$-median clustering problem in which $n$ pointsarrive online and must be irrevocably assigned to a cluster on arrival. Asthere are lower bound instances that show that an online algorithm cannotachieve a competitive ratio that is a function of $n$ and $k$, we consider abeyond worst-case analysis model in which the algorithm is provided a prioriwith a predicted budget $B$ that upper bounds the optimal objective value. Wegive an algorithm that achieves a competitive ratio that is exponential in thethe number $k$ of clusters, and show that the competitive ratio of everyalgorithm must be linear in $k$. To the best of our knowledge this is the firstinvestigation in the literature that considers cluster consistency usingcompetitive analysis.

Online $k$-Median with Consistent Clusters