  Prefix aggregation operation (also called scan), and its particular case,
prefix summation, is an important parallel primitive and enjoys a lot of
attention in the research literature. It is also used in many algorithms as one
of the steps.
  Aggregation over dominated points in $\mathbb{R}^m$ is a multidimensional
generalisation of prefix aggregation. It is also intensively researched, both
as a parallel primitive and as a practical problem, encountered in
computational geometry, spatial databases and data warehouses.
  In this paper we show that, for a constant dimension $m$, aggregation over
dominated points in $\mathbb{R}^m$ can be computed by $O(1)$ basic operations
that include sorting the whole dataset, zipping sorted lists of elements,
computing prefix aggregations of lists of elements and flat maps, which expand
the data size from initial $n$ to $n\log^{m-1}n$.
  Thereby we establish that prefix aggregation suffices to express aggregation
over dominated points in more dimensions, even though the latter is a
far-reaching generalisation of the former. Many problems known to be
expressible by aggregation over dominated points become expressible by prefix
aggregation, too.
  We rely on a small set of primitive operations which guarantee an easy
transfer to various distributed architectures and some desired properties of
the implementation.
