Dominant and K Nearest Probabilistic Skylines

By definition, objects that are skyline points cannot be compared with each other. Yet, thanks to the probabilistic skyline model, skyline points with repeated observations can now be compared. In this model, each object will be assigned a value to denote for its probability of being a skyline point. When we are using this model, some questions will naturally be asked: (1) Which of the objects have skyline probabilities larger than a given object? (2) Which of the objects are the K nearest neighbors to a given object according to their skyline probabilities? (3) What is the ranking of these objects based on their skyline probabilities? Up to our knowledge, no existing work answers any of these questions. Yet, answering them is not trivial. For just a medium-size dataset, it may take more than an hour to obtain the skyline probabilities of all the objects in there. In this paper, we propose a tree called SPTree that answers all these queries efficiently. SPTree is based on the idea of space partition. We partition the dataspace into several subspaces so that we do not need to compute the skyline probabilities of all objects. Extensive experiments are conducted. The encouraging results show that our work is highly feasible.