Dynamic Top-$k$ Dominating Queries

Let $\mathcal{S}$ 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 $\mathcal{S}$. 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.