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Efficient Algorithms for Maximum Regression Depth

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


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(n ) time and space algorithm computes directed depth of all points in d dimensions. Properties of undirected depth lead to an O(n log 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

Year: 2002
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