Pedersen et al. (1999) propose a method for adding null elements which overcomes
this drawback. The central idea is to allow adding different nulls, which may be the
result of breaking up some of the original elements of the dimension. The nulls are
interpreted as regular elements and the resulting dimension is homogeneous, so the
framework of aggregate navigation can be applied.
The transformation has low and practical complexity and can be applied to OLAP data
in a preprocessing stage before loading the data cube. An algorithm, called MakeCovering,
performs the transformation. The algorithm has polynomial time complexity
on the size of the dimension. More precisely, the algorithm takes O(k2nlogn), where
k is the number of categories, and n is the size of the largest rollup relation.
In many situations the null elements have a low interference with the original data;
and therefore handling heterogeneity with null elements has practical applicability
in many cases. Intuitively, in such cases, the null elements play the role of the other
or the unknown class. However, in worst-case scenarios, the transformation may
lead to dimensions with many new null elements per category. In these cases, the
number of rows of the data cube and cube views may be considerably increased due
to the null elements. As some original elements of the dimension may be broken up
into different nulls, the semantics of the original dimension may be altered.
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