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(kn2) 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.
CITATION STYLE
Banerjee, I., & Richards, D. (2016). Computing maximal layers of points in Ef(N). In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 9644, pp. 138–151). Springer Verlag. https://doi.org/10.1007/978-3-662-49529-2_11
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