Lukas Drexler
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View article: Connected k-Center and k-Diameter Clustering
Connected k-Center and k-Diameter Clustering Open
Motivated by an application from geodesy, we study the connected k-center problem and the connected k-diameter problem . The former problem has been introduced by Ge et al. (ACM Trans Knowl Discov Data 2(2):1–35, 2008. https://doi.org/10.1…
View article: Local Search k-means++ with Foresight
Local Search k-means++ with Foresight Open
Since its introduction in 1957, Lloyd's algorithm for $k$-means clustering has been extensively studied and has undergone several improvements. While in its original form it does not guarantee any approximation factor at all, Arthur and Va…
View article: FPT Approximations for Fair k-Min-Sum-Radii
FPT Approximations for Fair k-Min-Sum-Radii Open
We consider the k-min-sum-radii (k-MSR) clustering problem with fairness constraints. The k-min-sum-radii problem is a mixture of the classical k-center and k-median problems. We are given a set of points P in a metric space and a number k…
View article: Clustering Graphs of Bounded Treewidth to Minimize the Sum of Radius-Dependent Costs
Clustering Graphs of Bounded Treewidth to Minimize the Sum of Radius-Dependent Costs Open
We consider the following natural problem that generalizes min-sum-radii clustering: Given is $k\in\mathbb{N}$ as well as some metric space $(V,d)$ where $V=F\cup C$ for facilities $F$ and clients $C$. The goal is to find a clustering give…
View article: Approximating Fair $k$-Min-Sum-Radii in Euclidean Space
Approximating Fair $k$-Min-Sum-Radii in Euclidean Space Open
The $k$-center problem is a classical clustering problem in which one is asked to find a partitioning of a point set $P$ into $k$ clusters such that the maximum radius of any cluster is minimized. It is well-studied. But what if we add up …
View article: Connected k-Center and k-Diameter Clustering
Connected k-Center and k-Diameter Clustering Open
Motivated by an application from geodesy, we study the connected k-center problem and the connected k-diameter problem. These problems arise from the classical k-center and k-diameter problems by adding a side constraint. For the side cons…