Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2503.02715 |
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Inhaltsangabe:
- We consider the $k$-center problem on the space of fixed-size point sets in the plane under the $L_{\infty}$-bottleneck distance. While this problem is motivated by persistence diagrams in topological data analysis, we illustrate it as a \emph{Restaurant Supply Problem}: given $n$ restaurant chains of $m$ stores each, we want to place supermarket chains, also of $m$ stores each, such that each restaurant chain can select one supermarket chain to supply all its stores, ensuring that each store is matched to a nearby supermarket. How many supermarket chains are required to supply all restaurants? We address this questions under the constraint that any two restaurant chains are close enough under the $L_{\infty}$-distance to be satisfied by a single supermarket chain. We provide both upper and lower bounds for this problem and investigate its computational complexity.