Dynamic Processing of Dominating Queries with Performance Guarantees

The top-k dominating query returns the k database objects with the highest score with respect to their dominance score. The dominance score of an object p is simply the number of objects dominated by p, based on minimization or maximization preferences on the attribute values. Each object (tuple) is represented as a point in a multidimensional space, and therefore, the number of attributes equals the number of dimensions. The top-k dominating query combines the dominance concept of skyline queries with the ranking function of top-k queries and can be used as an important tool in multi-criteria decision making systems. In this work, we focus on the 2-dimensional space and present, for the first time, novel algorithms for top-k dominating query processing in main memory with non-trivial asymptotic guarantees. In particular, we focus on both the semi-dynamic case (only insertions are allowed) and the fully-dynamic case (insertions and deletions are supported). We perform a detailed cost analysis regarding the worst-case complexity of preprocessing, the worst-case complexity for the query cost and the worst-case and amortized complexity for updates (insertions and deletions) focusing on the RAM computation model. Our solutions require space linear with the number of points, which is very important especially for modern applications which manipulate massive datasets. In addition, we discuss the case of the word-RAM computation model, where slightly better results are obtained.