Fully-dynamic orthogonal range reporting on RAM

In a natural variant of the comparison model, we show that there exists aconstant ω<1 such that the fully-dynamic d -dimensional orthogonal range reporting problem for d≥2 can be solved in time O(log^ω+d−2n) for updates and time O((logn/loglogn)^d−1+r) for queries. Here n is the number of points stored and r is the number of points reported. The space usage is O(nlog^ω+d−2n). In the standard comparison model the result holds for d≥3.