The problem of Skyline computation has attracted considerable research attention in the last decade. A Skyline query selects those tuples from a dataset that are optimal with respect to a set of designated preference attributes. Since multicore processors are going mainstream, it has become imperative to develop parallel algorithms, which fully exploit the advantages of such modern hardware architectures. In this paper, the authors present high-performance parallel Skyline algorithms based on the lattice structure generated by a Skyline query. For this, they propose different evaluation strategies and compare several data structures for the parallel evaluation of Skyline queries. The authors present novel optimization techniques for lattice based Skyline algorithms based on pruning and removing one unrestricted attribute domain. They demonstrate through comprehensive experiments on synthetic and real datasets that their new algorithms outperform state-of-the-art multicore Skyline techniques for low-cardinality domains. The authors' algorithms have linear runtime complexity and fully play on modern hardware architectures.