need a data structure that supports point location queries on a planar orthogonal subdivision of size $O(m/t)$ [@Chan13]. This data structure uses $O(m/\log^5n)$ bits. Hence our dominance data structure uses $O(m\log \log n)$ bits. We need only one instance of range selection data structure for all slabs; in this section we use the variant that consumes $O(n\log n)$ bits of space. Hence the total space usage of the global data structure is not affected.

We also use range selection to access points stored in the slabs of size $O(\log^8 n)$ of the grid structure. The number of points in every slab that is not divided further is $\Omega(\log^4 n)$. Since every point is stored in $O(\log n/\log\log n)$ recursive structures, the number of slabs is bounded by $O(n/\log^3 n)$. Since the range selection data structure requires $O(\log^{2+{\varepsilon}} n$ bits per rectangle (i.e., per slab), the space usage of the range selection data structure is $O(n)$.

#### Two-Dimensional Range Minima Queries.

Our data structure for five-sided queries can be easily modified to support range minima queries. We can adjust the slab dominance data structure, described in this section, so that it supports 2-d dominance minima queries. We use the same shallow 