Computing the maximum bichromatic discrepancy is an interesting theoretical problem with important applications in computational learning theory, computational geometry and computer graphics. In this paper we give algorithms to compute the maximum bichromatic discrepancy for simple geometric ranges, including rectangles and halfspaces. In addition, we give extensions to other discrepancy problems.

This technical report has been published as

Computing the maximum bichromatic discrepancy, with applications to computer graphics and machine learning. David P. Dobkin, Dimitrios Gunopulos, Wolfgang Maass, J. of Computer and System Sciences, vol 52, no. 3, 453-470, June 1996.