Computing Half-plane and Strip Discrepancy of Planar Point Sets

Abstract We present efficient algorithms for two problems concerning the discrepancy of a set S of n points in the unit square in the plane. First, we describe an algorithm for maintaining the half-plane discrepancy of S under insertions and deletions of points. The algorithm runs in O( n log n ) worst-case time per update, and it requires only relatively simple data structures. Second, we give an algorithm that computes the strip discrepancy of S in O( n 2 α ( n )log n ) time, where α ( n ) is the extremely slowly growing functional inverse of Ackermann's function.