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Aggregation: Data Cubes and Materialized Views

Not every data warehouse is necessarily a column store: traditional row-oriented databases and a few other architectures are also used. However, columnar storage can be significantly faster for ad hoc analytical queries, so it is rapidly gaining popularity [51, 63].

Another aspect of data warehouses that is worth mentioning briefly is materialized aggregates. As discussed earlier, data warehouse queries often involve an aggregate function, such as COUNT, SUM, AVG, MIN, or MAX in SQL. If the same aggregates are used by many different queries, it can be wasteful to crunch through the raw data every time. Why not cache some of the counts or sums that queries use most often?

One way of creating such a cache is a materialized view. In a relational data model, it is often defined like a standard (virtual) view: a table-like object whose contents are the results of some query. The difference is that a materialized view is an actual copy of the query results, written to disk, whereas a virtual view is just a shortcut for writing queries. When you read from a virtual view, the SQL engine expands it into the view’s underlying query on the fly and then processes the expanded query.

When the underlying data changes, a materialized view needs to be updated, because it is a denormalized copy of the data. The database can do that automatically, but such updates make writes more expensive, which is why materialized views are not often used in OLTP databases. In read-heavy data warehouses they can make more sense (whether or not they actually improve read performance depends on the individual case).

A common special case of a materialized view is known as a data cube or OLAP cube [64]. It is a grid of aggregates grouped by different dimensions. Figure 3-12 shows an example.

Two dimensions of a data cube, aggregating data by summing

Figure 3-12. Two dimensions of a data cube, aggregating data by summing.

Imagine for now that each fact has foreign keys to only two dimension tables—in Figure 3-12, these are date and product. You can now draw a two-dimensional table, with dates along one axis and products along the other. Each cell contains the aggregate (e.g., SUM) of an attribute (e.g., net_price) of all facts with that date-product combination. Then you can apply the same aggregate along each row or column and get a summary that has been reduced by one dimension (the sales by product regardless of date, or the sales by date regardless of product).

In general, facts often have more than two dimensions. In Figure 3-9 there are five dimensions: date, product, store, promotion, and customer. It’s a lot harder to imagine what a five-dimensional hypercube would look like, but the principle remains the same: each cell contains the sales for a particular date-product-store-promotion- customer combination. These values can then repeatedly be summarized along each of the dimensions.

The advantage of a materialized data cube is that certain queries become very fast because they have effectively been precomputed. For example, if you want to know the total sales per store yesterday, you just need to look at the totals along the appropriate dimension—no need to scan millions of rows.

The disadvantage is that a data cube doesn’t have the same flexibility as querying the raw data. For example, there is no way of calculating which proportion of sales comes from items that cost more than $100, because the price isn’t one of the dimensions. Most data warehouses therefore try to keep as much raw data as possible, and use aggregates such as data cubes only as a performance boost for certain queries.

 
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