Slicing – Sizing – Rising

A Theory of Datacube and Pivot-Tables

November 12, 2023

A pivot table is a powerful means to represent structured, multi-dimensional data on a two-dimensional space. They enable a user to show a large amount of structured data from different angles and perspectives.

This paper gives a survey and implementation in LPL on datacube and pivot-tables in order to understand and use OLAP functionalities. It is argued that slicing, sizing, and rising are fundamental data operations of multidimensional datacubes. They are the basic building block of every OLAP tool, hence our efforts are concentrated on them. The datacube operations are explained as functions which transforms n-dimensional datacubes into datacubes of dimensions less, equal or higher than n. All operations are viewed in this perspective. This reduces various kinds of OLAP-operations considerably and looks at them in a new unified way, which also might be interesting in implementing OLAP-tools.

Then this paper exposes the connections of n-dimensional datacubes with their many 2-dimensional representations, the pivot-tables. The many different pivot-table representations of an n-dimensional datacube are also understood in a unified way, such that all representations can be generated from each other by a very limited number of operations on the datacube which could be subsumed under the general operator pivoting. It is shown how a datacube of any dimension is transformed into any pivot-table representation using just pivoting and the mentioned cube operations slicing, sizing, and rising.

It’s a little-known fact... Shakespeare was working on an Excel spreadsheet

and created a formula that inspired one of his most famous formula:

=OR(B2, NOT(B2))

Spreadsheet Poem:

You may spreadsheet in columns

You may spreadsheet in rows

But the more you spreadsheet

The faster it grows.