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In fact, bitmap indices are useful for selections mainly when there are selections on multiple keys Suppose we create a bitmap index on attribute income-level, which we described earlier, in addition to the bitmap index on gender Consider now a query that selects women with income in the range 10, 000 19, 999 This query can be expressed as gender=f income-level=L2 (r) To evaluate this selection, we fetch the bitmaps for gender value f and the bitmap for income-level value L2, and perform an intersection (logical-and) of the two bitmaps In other words, we compute a new bitmap where bit i has value 1 if the ith bit of the two bitmaps are both 1, and has a value 0 otherwise In the example in Figure 1233, the intersection of the bitmap for gender = f (01101) and the bitmap for income-level = L1 (10100) gives the bitmap 00100 Since the rst attribute can take 2 values, and the second can take 5 values, we would expect only about 1 in 10 records, on an average, to satisfy a combined condition on the two attributes If there are further conditions, the fraction of records satisfying all the conditions is likely to be quite small The system can then compute the query result by nding all bits with value 1 in the intersection bitmap, and retrieving the corresponding records If the fraction is large, scanning the entire relation would remain the cheaper alternative Another important use of bitmaps is to count the number of tuples satisfying a given selection Such queries are important for data analysis For instance, if we wish to nd out how many women have an income level L2, we compute the intersection of the two bitmaps, and then count the number of bits that are 1 in the intersection bitmap We can thus get the desired result from the bitmap index, without even accessing the relation Bitmap indices are generally quite small compared to the actual relation size Records are typically at least tens of bytes to hundreds of bytes long, whereas a single bit represents the record in a bitmap Thus the space occupied by a single bitmap is usually less than 1 percent of the space occupied by the relation For instance, if the record size for a given relation is 100 bytes, then the space occupied by a single bitmap would be 1 of 1 percent of the space occupied by the relation If an attribute A 8 of the relation can take on only one of 8 values, a bitmap index on attribute A would consist of 8 bitmaps, which together occupy only 1 percent of the size of the relation.

The McGraw Hill Companies, 2001

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12

Deletion of records creates gaps in the sequence of records, since shifting records (or record numbers) to ll gaps would be extremely expensive To recognize deleted records, we can store an existence bitmap, in which bit i is 0 if record i does not exist and 1 otherwise We will see the need for existence bitmaps in Section 12942 Insertion of records should not affect the sequence numbering of other records Therefore, we can do insertion either by appending records to the end of the le or by replacing deleted records

The superposition theorem tells us that the total current is due to the sums of the currents due to each individual source alone That is I1 = I1 + I1 = Some notes about superposition: 20 35 15 = A 38 38 38

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