I/O-optimal categorical 3-sided skyline queries

The skyline of a set of two-dimensional points is the subset of points not dominated by any other point. In this paper, we consider a set of two-dimensional points (in rank space) that are assigned an additional category, or color. The goal is to preprocess these points so that given a three-sided region of the form [a, b] x [tau, infinity] we can return the set of distinct colors on the skyline of the queried region. We approach this problem in the external memory model and present an I/O-optimal data structure that answers a query using O (1 + k/B) I/Os and requires O (n log* n) words of space, where n is the number of points, k is the size of the solution, and B is the block size. Additionally, we provide a space-time trade-off by presenting a data structure that answers a query using O ((log* n)(2) + k/B) I/Os and requires O (n) words of space. (C) 2021 Published by Elsevier B.V.