Computing Enclosing Depth
<|reference_start|>Computing Enclosing Depth: Enclosing depth is a recently introduced depth measure which gives a lower bound to many depth measures studied in the literature. So far, enclosing depth has only been studied from a combinatorial perspective. In this work, we give the first algorithms to compute the enclosing depth of a query point with respect to a data point set in any dimension. In the plane we are able to optimize the algorithm to get a runtime of O(n log n). In constant dimension, our algorithms still run in polynomial time.<|reference_end|>
@article{gärtner2024computing,
    title={Computing Enclosing Depth},
    author={Bernd G"artner and Fatime Rasiti and Patrick Schnider},
    journal={arXiv preprint arXiv:2402.12371},
    year={2024},
    archivePrefix={arXiv},
    eprint={2402.12371},
    primaryClass={cs.CG}
}