On finding skylines in external memory

We consider the skyline problem (a.k.a. the maxima problem), which has been extensively studied in the database community. The input is a set P of d-dimensional points. A point dominates another if the former has a lower coordinate than the latter on every dimension. The goal is to find the skyline, which is the set of points p ∈ P such that p is not dominated by any other data point. In the external-memory model, the 2-d version of the problem is known to be solvable in O((N/B)log_M/B(N/B)) I/Os, where N is the cardinality of P, B the size of a disk block, and M the capacity of main memory. For fixed d ≥ 3, we present an algorithm with I/O-complexity O((N/B)logd-2/M/B(N/B)). Previously, the best solution was adapted from an in-memory algorithm, and requires O((N/B) logd-2/2(N/M)) I/Os.