Abstract

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. 1 Introduction The main theme of this paper is to present efficient algorithms that solve the problem of computing the maximum bichromatic discrepancy for axis oriented rectangles. This problem arises naturally in different areas of computer science, such as computational learning theory, computational geometry and computer graphics ([Ma], [DG]), and has applications in all these areas. In computational learning theory, the problem of agnostic PAC-learning with simple geometric hypotheses can be reduced to the problem of computing the maximum bichromatic discrepancy for simple geometric ra...

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