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I am looking for state-of-the-art results on dynamic dominance reporting. In the dynamic dominance reporting problem, we have a set of k dimensional points and the goal is to maintain a data structure under insertions and deletions of points. The data structure is used to find the count of/enumerate all points that are dominated by a given query point.

A quick search on Google scholar shows a lot of results on dynamic orthogonal range reporting but I wasn't able to find much for the dynamic dominance reporting setting. A recent paper shows result for dynamic dominance reporting when $k=2$. Are there any algorithms/lower bounds known for general $k$ (or even $k \geq 3$)?

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