Efficient skyline retrieval with arbitrary similarity measures

A skyline query returns a set of objects that are not dominated by other objects. An object is said to dominate another if it is closer to the query than the latter on all factors under consideration. In this paper, we consider the case where the similarity measures may be arbitrary and do not necessarily come from a metric space. We first explore middleware algorithms, analyze how skyline retrieval for non-metric spaces can be done on the middleware backend, and lay down a necessary and sufficient stopping condition for middleware-based skyline algorithms. We develop the Balanced Access Algorithm, which is provably more IO-friendly than the state-of-the-art algorithm for skyline query processing on middleware and show that BAA outperforms the latter by orders of magnitude. We also show that without prior knowledge about data distributions, it is unlikely to have a middleware algorithm that is more IO-friendly than BAA. In fact, we empirically show that BAA is very close to the absolute lower bound of IO costs for middleware algorithms. Further, we explore the non-middleware setting and devise an online algorithm for skyline retrieval which uses a recently proposed value space index over non-metric spaces (AL-Tree [10]). The AL-Tree based algorithm is able to prune subspaces and efficiently maintain candidate sets leading to better performance. We compare our algorithms to existing ones which can work with arbitrary similarity measures and show that our approaches are better in terms of computational and disk access costs leading to significantly better response times.