Computing Enclosing Depth

Bernd Gärtner; Fatime Rasiti; Patrick Schnider

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arXiv · 2402.12371

Computing Enclosing Depth

Bernd Gärtner·Fatime Rasiti·Patrick Schnider

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Abstract

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.

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Bernd Gärtner, Fatime Rasiti, Patrick Schnider. 2024-02-19. Computing Enclosing Depth. https://arxiv.org/abs/2402.12371

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