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CHAPTER 9 QUERY TRANSFORMATION
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bitmap on the fact1 table. We scan each dimension table in turn to pick up the primary key values the primary key values (when sorted) allow us to walk along the corresponding bitmap index of the fact table, picking up the relevant bitmap sections and merging them into a single bitstream. After we have done this for all three dimensions, we have three bitstreams that we can apply the bitmap and operation to, converting any resulting bits to their corresponding rowid. The line marked with the +++ is particularly important. In this line, the optimizer tells us how many relevant rows it thinks there are in the fact table: card = 53 (which happens to be correct thanks to the rather contrived way that I constructed the data). Compare this with the cardinality reported from the brutal hash join: card = 423404. The difference is quite significant. In fact, the divergence gets worse, because the final cardinality reported for the complete query is only 11 according to the star transformation plan. The discrepancy arises from two distinct factors. First, there seems to be a bug in the code that handles the bitmap and portion of the plan. The reason for the strange names of the dimensions is that I had 23, 31, and 53 distinct values of each column appearing in the fact1 table (plus a lot of other values in the dimension tables to pad them up a bit). The predicates I had on the dimension tables selected 20 rows each, so in theory they should have selected 20 sections from each of the bitmaps on the fact table. However, the optimizer s arithmetic is based on the absolute selectivity of the bitmap indexes, and doesn t allow for the actual number of bitmap sections identified by each of the dimension tables. I had 2,000,000 rows in the fact table, and the selectivities of my three bitmap indexes were 23, 31, and 53, respectively, so the optimizer calculated the cardinality of the bitmap access step as 2,000,000 / (23 * 31 * 53) = 52.925. This happens to be the correct answer in my example, but only because I had rigged my dimension tables so that 19 of the 20 values that I had chosen would not appear in the fact table. The second factor that comes into play arises from the fact that star transformations obey normal join arithmetic. After using the bitmap and mechanism to identify the starting set in the fact1 table, the optimizer simply applied the standard join arithmetic to the task of joining back the three dimension tables. And that s highly questionable, of course, because we ve already done that arithmetic once to derive the starting number of rows every row we join back is doing the join to extend the row length, and there is no question of rows being eliminated or multiplied by the second join pass. Star transformations get the wrong cardinality because they apply join selectivities twice! We don t even have to know how the join arithmetic works to see this second factor in action; we can just use ratios (horror, shock, gasp) to prove the point. In the first execution plan (without the star transformation), I started with 2,000,000 rows, and after three joins the cardinality was down to 423,404 a factor of 4.7236. In the execution plan for the star join, I have an estimated 53 rows as the starting cardinality after the bitmap and before doing the joins back to the dimensions. Divide this by the same 4.7236, and you get 11.2 and the final cardinality after the joins is 11. If you check the 10053 trace file when you have enabled star transformations, you will find that there are several sections of general plans. The first is the normal (no-transformation) plan, followed by separate plans for each of the dimension tables in turn (each with its own join order[1]), and finally this heading:
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