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

Aggregating over Dominated Points by Sorting, Scanning, Zip and Flat Maps