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ITIS 5160 Indexing
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Indexing datacubes Objective: speed queries up.
Traditional databases (OLTP): B-Trees Time and space logarithmic to the amount of indexed keys. Dynamic, stable and exhibit good performance under updates. (But OLAP is not about updates….) Bitmaps: Space efficient Difficult to update (but we don’t care in DW). Can effectively prune searches before looking at data.
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Bitmaps R = (…., A,….., M) R (A) B8 B7 B6 B5 B4 B3 B2 B1 B0
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Query optimization Consider a high-selectivity-factor query with predicates on two attributes. Query optimizer: builds plans (P1) Full relation scan (filter as you go). (P2) Index scan on the predicate with lower selectivity factor, followed by temporary relation scan, to filter out non-qualifying tuples, using the other predicate. (Works well if data is clustered on the first index key). (P3) Index scan for each predicate (separately), followed by merge of RID.
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Query optimization (continued)
tn Index Pred1 Blocks of data (P2) Tuple list1 (P3) Merged list Pred. 2 t1 tn Index Pred2 Tuple list2 answer
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Query optimization (continued)
When using bitmap indexes (P3) can be an easy winner! CPU operations in bitmaps (AND, OR, XOR, etc.) are more efficient than regular RID merges: just apply the binary operations to the bitmaps (In B-trees, you would have to scan the two lists and select tuples in both -- merge operation--) Of course, you can build B-trees on the compound key, but we would need one for every compound predicate (exponential number of trees…).
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Bitmaps and predicates
A = a1 AND B = b2 Bitmap for a1 Bitmap for b2 Bitmap for a1 and b2 = AND
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Tradeoffs Dimension cardinality small dense bitmaps
Dimension cardinality large sparse bitmaps Compression (decompression)
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Star-Joins Select F.S, D1.A1, D2.A2, …. Dn.An Likely strategy:
from F,D1,D2,Dn where F.A1 = D1.A1 F.A2 = D2.A2 … F.An = Dn.An and D1.B1 = ‘c1’ D2.B2 = ‘p2’ …. Likely strategy: For each Di find suitable values of Ai such that Di.Bi = ‘xi’ (unless you have a bitmap index for Bi). Use bitmap index on Ai’ values to form a bitmap for related rows of F (OR-ing the bitmaps). At this stage, you have n such bitmaps, the result can be found AND-ing them.
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Bitmaps R = (…., A,….., M) value-list index
R (A) B8 B B6 B5 B4 B3 B2 B1 B0
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Example sequence <3,3> value-list index (equality)
R (A) B22 B12 B02 B21 B11 B01 (1x3+0)
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Encoding scheme Equality encoding: all bits to 0 except the one that corresponds to the value Range Encoding: the vi rightmost bits to 0, the remaining to 1
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Range encoding single component, base-9
R (A) B8 B B6 B5 B4 B3 B2 B1 B0
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RangeEval Evaluates each range predicate by computing two bitmaps: BEQ bitmap and either BGT or BLT RangeEval-Opt uses only <= A < v is the same as A <= v-1 A > v is the same as Not( A <= v) A >= v is the same as Not (A <= v-1)
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Example (revisited) sequence <3,3> value-list index(Equality)
R (A) B22 B12 B02 B21 B11 B01 (1x3+0)
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Example sequence <3,3> range-encoded index
R (A) B12 B B11 B01
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RangeEval-OPT
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