What makes access to OLAP Cubes/Datamarts and similar datastructures, faster than to relational databases?
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I would say mainly because of different purposes.
OLAP cubes / datamarts are used mainly in read mode for data analysis by business users whereas I’m assuming when mentioning relational DBs you’re talking about OLTP usage requiring for example ACID transactions.
Those different purposes means:
In addition OLAP has a more powerful language (MDX) with higher concepts like hierarchical dimensions; implementations can take advantage of that and propose internal data structures optimized for those concepts.
My 2 cents.