Computing Maximal Layers of Points in Eᶠ⁽ⁿ⁾

In this paper we present a randomized algorithm for computing the collection of maximal layers for a point set in Ek (k = f(n)). The input to our algorithm is a point set P = {p1,..., pn} with pi ∈ Ek. The proposed algorithm achieves a runtime of O (formula presented) when P is a random order and a runtime of O(formula presented) for an arbitrary P. Both bounds hold in expectation. Additionally, the run time is bounded by O(knk) in the worst case. This is the first non-trivial algorithm whose run-time remains polynomial whenever f(n) is bounded by some polynomial in n while remaining sub-quadratic in n for constant k (in expectation). The algorithm is implemented using a new data-structure for storing and answering dominance queries over the set of incomparable points.