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We consider the problem of computing the \emph{distance-based representativeskyline} in the plane, a problem introduced by Tao, Ding, Lin and Pei [Proc.25th IEEE International Conference on Data Engineering (ICDE), 2009] andindependently considered by Dupin, Nielsen and Talbi [Optimization and Learning- Third International Conference, OLA 2020] in the context of multi-objectiveoptimization. Given a set $P$ of $n$ points in the plane and a parameter $k$,the task is to select $k$ points of the skyline defined by $P$ (also known asPareto front for $P$) to minimize the maximum distance from the points of theskyline to the selected points. We show that the problem can be solved in$O(n\log h)$ time, where $h$ is the number of points in the skyline of $P$. Wealso show that the decision problem can be solved in $O(n\log k)$ time and theoptimization problem can be solved in $O(n \log k + n \operatorname{loglog} n)$time. This improves previous algorithms and is optimal for a large range ofvalues of $k$.

Faster Distance-Based Representative Skyline and $k$-Center Along Pareto Front in the Plane