Dynamic Top-$k$ Dominating Queries

Let S be a dataset of n 2-dimensional points. The top-k dominating query aims to report the k points that dominate the most points in S . A point p dominates a point q iff all coordinates of p are smaller than or equal to those of q and at least one of them is strictly smaller. The top-k dominating query combines the dominance concept of maxima 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 propose novel algorithms for answering semi-dynamic (insertions only) and fully dynamic (insertions and deletions) top-k dominating queries. To the best of our knowledge, this is the first work towards handling (semi-)dynamic top-k dominating queries that offers algorithms with asymptotic guarantees regarding their time and space cost.