Approximating majority depth

Authors:
Dan Chen;Pat Morin
Affiliations:
-;-
Venue:
Computational Geometry: Theory and Applications
Year:
2013

Citing 4
Cited 0

Algorithms in combinatorial geometry

Algorithms in combinatorial geometry
Point sets with many k-sets

Proceedings of the sixteenth annual symposium on Computational geometry
Dynamic Planar Convex Hull

FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Optimal Partition Trees

Discrete & Computational Geometry - Special Issue: 26th Annual Symposium on Computational Geometry; Guest Editor: David Kirkpatrick

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the problem of approximating the majority depth (Liu and Singh, 1993) of a point q with respect to an n-point set, S, by random sampling. At the heart of this problem is a data structures question: How can we preprocess a set of n lines so that we can quickly test whether a randomly selected vertex in the arrangement of these lines is above or below the median level. We describe a Monte Carlo data structure for this problem that can be constructed in O(nlogn) time, can answer queries in O((logn)^4^/^3) expected time, and answers correctly with high probability.