Sparse and dense are a property of the values of an attribute.
Sparse is better than Dense
Data is normally stored in sparse form. If no value exists for a given combination of dimension values, no row exists in the fact table. For example, if not every product is sold in every market. In this case, Market and Product are sparse dimensions.
Most multidimensional databases may also contain dense dimensions. A fact table is considered to have dense data if it has (of a high probability to have) one row for every combination of its associated dimension levels.
A typical situation in the SH schema with a sparse dimension is shown in the following example, which computes the weekly sales and year-to-date sales for the product Bounce for weeks 20-30 in 2000 and 2001:
SELECT SUBSTR(p.Prod_Name,1,15) Product_Name, t.Calendar_Year Year, t.Calendar_Week_Number Week, SUM(Amount_Sold) Sales FROM Sales s, Times t, Products p WHERE s.Time_id = t.Time_id AND s.Prod_id = p.Prod_id AND p.Prod_name IN ('Bounce') AND t.Calendar_Year IN (2000,2001) AND t.Calendar_Week_Number BETWEEN 20 AND 30 GROUP BY p.Prod_Name, t.Calendar_Year, t.Calendar_Week_Number ORDER BY product_name, year, week ASC
PRODUCT_NAME YEAR WEEK SALES --------------- ---------- ---------- ---------- Bounce 2000 20 801 Bounce 2000 21 4062.24 Bounce 2000 22 2043.16 Bounce 2000 23 2731.14 Bounce 2000 24 4419.36 ---- Miss one row for the week 25 ---- Miss one row for the week 26 Bounce 2000 27 2297.29 Bounce 2000 28 1443.13 Bounce 2000 29 1927.38 Bounce 2000 30 1927.38 Bounce 2001 20 1483.3 Bounce 2001 21 4184.49 Bounce 2001 22 2609.19 Bounce 2001 23 1416.95 Bounce 2001 24 3149.62 Bounce 2001 25 2645.98 ---- Miss one row for the week 26 Bounce 2001 27 2125.12 ---- Miss one row for the week 28 Bounce 2001 29 2467.92 Bounce 2001 30 2620.17
In this example, we would expect 22 rows of data (11 weeks each from 2 years) if the data were dense. However we get only 18 rows because weeks 25 and 26 are missing in 2000, and weeks 26 and 28 in 2001.
You may want to view the data in dense form, with rows for all combination of dimension values displayed even when no fact data exist for them.
For example, if a product did not sell during a particular time period, you may still want to see the product for that time period with zero sales value next to it.
If you are in a relational environment, you must perform a SQL densification: Continue to read ...
In a MOLAP environement, sparse data are not present.
In relational tables, records are only present for data that exists, whereas in a MOLAP cubes, an empty value is used where no data exists. The cube stores the real data values and whereas the empty values are easily addressable and queryable, they are not actually stored in the cube.
For example, you can easily refer to last month’s data value in a query even if that month has no data, but the empty value is not stored.
This highlights the very important feature of MOLAP cubes in that they operate as if they are fully populated with both actual data and zero data for all combinations possible of their attribute dimensions values.
This can have a very important benefit because it makes defining calculations easier as it can be assumed that all data points are present in the cube.
For example, the following formula can be defined even if there is no actual value, or physical storage used, for Tents in Feb2002:
nvl(sales('Feb2002','Tents'),0) - nvl(sales('Jan2002', 'Tents'), 0)
If the reporting requirements need to process null value rows, serious consideration should be given to using a MOLAP solution because they can handle this information by default rather than having to write a more complex densification SQL statement to generate the same result.