Practical approximation algorithm for the LMS line estimator

Two algorithms are presented for solving the problem of fitting a straight line to a finite collection of data points in a plane. The first algorithm is a conceptually simple randomized Las Vegas approximation algorithm for Rousseeuw's least median-of-squares (LMS) line estimator which runs in O(n log n) time. However, this algorithm relies on somewhat complicated data structures to achieve its efficiency. The second algorithm is a practical randomized algorithm for LMS that uses simple data structures. Although this algorithm runs no slower than O(n² log n) time, there is empirical evidence that its running time on realistic data sets is much faster. The latter algorithm provides the efficiency of a Monte Carlo algorithm while ensuring accuracy.