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A method is proposed for least absolute deviations curve fitting. It may be used to obtain least absolute deviations fits of general linear regressions. As a special case it includes a minor variant of a method for fitting straight lines by least absolute deviations that was previously thought to possess no generalization. The method has been tested on a computer and was found on a range of problems to execute in as little as 1/3 the CPU time required by a published algorithm based on linear programming. More important, this advantage appears to increase indefinitely with the number of data points

Given disjoint sets PI, P2 ..... Pd in R a with n points in total, a hamsandwich cut is a hyperplane that simultaneously bisects the Pi. We present algorithms for finding ham-sandwich cuts in every dimension d > 1. When d = 2, the algorithm is optimal, having complexity O(n). For dimension d > 2, the bound on the running time is proportional to the worst-case time needed for constructing a level in an arrangement of n hyperplanes in dimension d-1. This, in turn, is related to the number of k-sets in R d-~. With the current estimates, we get complexity close to O(n 3/2) for d = 3, roughly O(n s/3) for d = 4, and O(n d-1-atd~) for some a(d) > 0 (going to zero as d increases) for larger d. We also give a linear-time algorithm for ham-sandwich cuts in R 3 when the three sets are suitably separated.

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