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2008

Efficient Algorithms for Maximum Regression Depth

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Efficient Algorithms for Maximum Regression Depth
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, which has been improved to an O(n log n) time algorithm by Langerman and Steiger [17]. Furthermore, we describe the structure of depth in the plane and higher dimensions and also give approximation algorithms for hyperplane arrangements and degenerate line arrangements.
Marc J. van Kreveld, Joseph S. B. Mitchell, Peter
Added 10 Dec 2010
Updated 10 Dec 2010
Type Journal
Year 2008
Where DCG
Authors Marc J. van Kreveld, Joseph S. B. Mitchell, Peter Rousseeuw, Micha Sharir, Jack Snoeyink, Bettina Speckmann
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