Efficient algorithms for maximum regression depth

Marc van Kreveld*, Joseph S.B. Mitchell, Peter Rousseeuw, Micha Sharir, Jack Snoeyink, Bettina Speckmann

*Corresponding author for this work

Research output: Contribution to conferencePaperpeer-review

12 Scopus citations


We investigate algorithmic questions that arise in the statistical problem of computing lines or hyperplanes of maximum regression depth among a set of n points. We work primarily with a dual representation and find points of maximum undirected depth in an arrangement of lines or hyperplanes. An O(nd) time and space algorithm computes directed depth of all points in d dimensions. Properties of undirected depth lead to an O(n log2 n) time and O(n) space algorithm for computing a point of maximum depth in two dimensions. We also give approximation algorithms for hyperplane arrangements and degenerate line arrangements.

Original languageEnglish
Number of pages10
StatePublished - 1999
Externally publishedYes
EventProceedings of the 1999 15th Annual Symposium on Computational Geometry - Miami Beach, FL, USA
Duration: 13 Jun 199916 Jun 1999


ConferenceProceedings of the 1999 15th Annual Symposium on Computational Geometry
CityMiami Beach, FL, USA


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