Computing the depth of a flat

Authors:
Marshall Bern
Affiliations:
Xerox PARC, 3333 Coyote Hill Rd., Palo Alto, CA
Venue:
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Year:
2001

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Abstract

We compute the regression depth of a k-flat in a set of n points in Rd, in time &Ogr;(nd-2 + n log n) for 1 ⪇ k ⪇ d - 2. This contrasts with a bound of &Ogr;(nd-1 + n log n) when k = 0 or k = d - 1.