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We consider the following problem related to both location theory and statistical linear regression. Given n points in the plane find a straight line L so as to minimize the weighted sum of the distances of the points to L relative to either the Euclidean metric or the l₁-metric. We present O ( n² log n ) and O ( nlog ² n ) time algorithms for the Euclidean and rectilinear cases, respectively.
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Megiddo et al. (1983) studied this question.
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