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CS 345: Topics in Data Warehousing

CS 345: Topics in Data Warehousing. Tuesday, October 19, 2004. Review of Thursday’s Class. Indexes B-Tree and Hash Indexes Clustered vs. Non-Clustered Covering Indexes Using Indexes in Query Plans Bitmap Indexes Index intersection plans Bitmap compression. Outline of Today’s Class.

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CS 345: Topics in Data Warehousing

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  1. CS 345:Topics in Data Warehousing Tuesday, October 19, 2004

  2. Review of Thursday’s Class • Indexes • B-Tree and Hash Indexes • Clustered vs. Non-Clustered • Covering Indexes • Using Indexes in Query Plans • Bitmap Indexes • Index intersection plans • Bitmap compression

  3. Outline of Today’s Class • Bitmap compression with BBC codes • Gaps and Tails • Variable byte-length encoding of lengths • Special handling of lone bits • Speeding up star joins • Cartesian product of dimensions • Semi-join reduction • Early aggregation

  4. Bitmap Compression • Compression via run length encoding • Just record number of zeros between adjacent ones • 00000001000010000000000001100000 • Store this as “7,4,12,0,5” • But: Can’t just write 11110011000101 • It could be 7,4,12,0,5. (111)(100)(1100)(0)(101) • Or it could be 3,25,8,2,1. (11)(11001)(1000)(10)(1) • Need structured encoding

  5. BBC Codes • Byte-aligned Bitmap Codes • Proposed by Antoshenkov (1994) • Used in Oracle • We’ll discuss a simplified variation • Divide bitmap into bytes • Gap bytes are all zeros • Tail bytes contain some ones • A chunk consists of some gap bytes followed by some tail bytes • Encode chunks • Header byte • Gap length bytes (sometimes) • Verbatim tail bytes (sometimes)

  6. BBC Codes • Number of gap bytes • 0-6: Gap length stored in header byte • 7-127: One gap-length byte follows header byte • 128-32767: Two gap-length bytes follow header byte • “Special” tail • Tail of a chunk is special if: • Tail consists of only 1 byte • The tail byte has only 1 non-zero bit • Non-special tails are stored verbatim (uncompressed) • Number of tail bytes is stored in header byte • Special tails are encoded by indicating which bit is set

  7. BBC Codes • Header byte • Bits 1-3: length of (short) gap • Gaps of length 0-6 don’t require gap length bytes • 111 = gap length > 6 • Bit 4: Is the tail special? • Bits 5-9: • Number of verbatim bytes (if bit 4=0) • Index of non-zero bit in tail byte (if bit 4 = 1) • Gap length bytes • Either one or two bytes • Only present if bits 1-3 of header are 111 • Gap lengths of 7-127 encoded in single byte • Gap lengths of 128-32767 encoded in 2 bytes • 1st bit of 1st byte set to 1 to indicate 2-byte case • Verbatim bytes • 0-15 uncompressed tail bytes • Number is indicated in header

  8. BBC Codes Example • 00000000 00000000 00010000 00000000 00000000 0000000000000000 00000000 00000000 00000000 00000000 0000000000000000 00000000 00000000 00000000 01000000 00100010 • Consists of two chunks • Chunk 1 • Bytes 1-3 • Two gap bytes, one tail byte • Encoding: (010)(1)(0100) • No gap length bytes since gap length < 7 • No verbatim bytes since tail is special • Chunk 2 • Bytes 4-18 • 13 gap bytes, two tail bytes • Encoding: (111)(0)(0010) 00001101 01000000 00100010 • One gap length byte gives gap length = 13 • Two verbatim bytes for tail • 01010100 11100010 00001101 01000000 00100010

  9. Expanding Query Plan Choices • “Conventional” query planner has limited options for executing star query • Join order: In which order should the dimensions be joined to the fact? • Join type: Hash join vs. Merge join vs. NLJ • Index selection: Can indexes support the joins? • Grouping strategy: Hashing vs. Sorting for grouping • We’ll consider extensions to basic join plans • Dimension Cartesian product • Semi-join reduction • Early aggregation

  10. Faster Star Queries • Consider this scenario • Fact table has 100 million rows • 3 dimension tables, each with 100 rows • Filters select 10 rows from each dimension • One possible query plan • Join fact to dimension A • Produce intermediate result with 10 million rows • Join result to dimension B • Produce intermediate result with 1 million rows • Join result to dimension C • Produce intermediate result with 100,000 rows • Perform grouping & aggregation • Each join is expensive • Intermediate results are quite large

  11. Dimension Cartesian Product • Consider this alternate plan: • “Join” dimensions A and B • Result is Cartesian product of all combinations • Result has 100 rows (10 A rows * 10 B rows) • “Join” result to dimension C • Another Cartesian product • 1000 rows (10 A rows * 10 B rows * 10 C rows) • Join result to fact table • Produce intermediate result with 100,000 rows • Perform grouping and aggregation • Computing Cartesian product is cheap • Few rows in dimension tables • Only one expensive join rather than three • Approach breaks down with: • Too many dimensions • Too many rows in each dimension satisfy filters

  12. Dimension Cartesian Product • Fact indexes can make Cartesian product approach even better • Suppose fact index exists with (A_key, B_key, C_key) as leading terms • Compute Cartesian product of A, B, C • Then use index to retrieve only the 0.1% of fact rows satisfying all filters • Joining fact to a single dimension table would require retrieving 10% of fact rows

  13. Cartesian Product Pros & Cons • Benefits of dimension Cartesian product • Fewer joins involve fact table or its derivatives • Leverage filtering power of multi-column fact indexes with composite keys • Drawbacks of dimension Cartesian product • Cartesian product result can be very large • More stringent requirements on fact indexes • Fact index must include all dimensions from Cartesian product to be useful • Dimension-at-a-time join plans can use thin fact index for initial join

  14. Semi-Join Reduction • Query plans involving semi-joins are common in distributed databases • Semi-join of A with B (A B) • All rows in A that join with at least 1 row from B • Discard non-joining rows from A • Attributes from B are not included in the result • Semi-join of B with A (B A) • All rows in B that join with at least 1 row from A • A B != B A • Identity: A B = A (B A)

  15. Semi-Join Reduction • To compute join of A and B on A.C1 = B.C2: • Server 1 sends C1 values from A to Server 2 • Server 2 computes semi-join of B with A • Server 2 sends joining B tuples to Server 1 • Server 1 computes join of A and B • Better sending simply sending entire B when: • Not too many B rows join with qualifying A rows A.C1 Server 1 Server 2 A B B

  16. Semi-Join Reduction for Data Warehouses • Goal is to save disk I/O rather than network I/O • Dimension table is “Server 1” • Fact table is “Server 2” • Fact table has single-column index on each foreign key column • Query plan goes as follows: • For each dimension table: • Determine keys of all rows that satisfy filters on that dimension • Use single-column fact index to look up RIDs of all fact rows with those dimension keys • Merge RID lists corresponding to each dimension • Retrieve qualifying fact rows • Join fact rows back to full dimension tables to learn grouping attributes • Perform grouping and aggregation

  17. Semi-Join Reduction • Semi-join query plan reduces size of intermediate results that must be joined • Intermediate results can be sorted, hashed more efficiently Dim Keys Server 1 Server 2 Dim Fact Fact

  18. Fact Index 1 2 Apply filters to eliminatenon-qualifying rows Dimension Table Dim.Keys Semi-joinfact index anddimension keys Generate list of dimension keys 3 = Intersect fact RID lists Semi-Join Reduction

  19. 4 Fact Table 5 Dimension Table FactRIDs Fact Rows Join back to dimensionsto bring in grouping attributes Lookup fact rowsbased on RIDs Semi-Join Reduction

  20. Semi-Join Reduction Pros &Cons • Benefits of semi-join reduction • Makes use of thin (1-column) fact indexes • Only relevant fact rows need be retrieved • Apply all filters before retrieving any fact rows • Drawbacks of semi-join reduction • Incur overhead of index intersection • Looking up fact rows from RIDs can be expensive • Random I/O • Only good when number of qualifying fact rows is small • Potential to access same dimension twice • Initially when generating dimension key list • Later when joining back to retrieve grouping columns

  21. Early Aggregation • Query plans we’ve considered do joins first, then grouping and aggregation • Sometimes “group by” can be handled in two phases • Perform partial aggregation early as a data reduction technique • Finish up the aggregation after completing all joins • Example: • SELECT Store.District, SUM(DollarSales)FROM Sales, Store, DateWHERE Sales.Store_key = Store.Store_keyAND Sales.Date_key = Date.Date_keyAND Date.Year = 2003GROUP BY Store.District • Lots of Sales rows, but fewer distinct (Store, Date) combinations • Early aggregation plan: • Group Sales by (Store, Date) & compute SUM(DollarSales) • Join result with Date dimension, filtered based on Year • Join result with Store dimension • Group by District & compute SUM(DollarSales)

  22. Conventional plan Join Sales and Date, filtering based on Year Result has 36 million rows Join result with Product Result has 36 million rows Group by District & compute aggregate Early aggregation plan Group Sales by (Date, Product) & compute aggregate Result has 100,000 rows Join result with Date Result has 36,500 rows Join result with District Result has 36,500 rows Group by District & compute aggregate Compare with Conventional Plan • Assumptions • Sales fact has 100 million rows • Store dimension has 100 rows • Date dimension has 1000 rows (365 in 2003)

  23. Early Aggregation Pros & Cons • Benefits of early aggregation • Initial aggregation can be fast with appropriate covering index • Leverage fact index on (Date, Store, DollarSales) • Result of early aggregation significantly smaller than fact table • Fewer rows • Fewer columns • Joins to dimension tables are cheaper • Because intermediate result is much smaller than fact table • Drawbacks of early aggregation • Can’t take advantage of data reduction due to filters • Prefer joins with highly selective filters (Date.Day = 'October 20, 2004') before early aggregation • Two aggregation steps instead of one • Adds additional overhead

  24. Summary • Three query planning techniques for star schema queries • Cartesian product of dimension tables • Useful when several dimensions are small, or filtered to a small number of rows • Cut down on the number of fact table joins • Semi-join reduction • Useful when AND of filters is quite selective, but individual filters are not • Only relevant rows from fact table are accessed • Doesn’t require a wide covering index • Early aggregation • Aggregation, like filtering, reduces size of tables • Useful when dimensions needed in query have low distinct cardinality • Which technique is best depends on individual query parameters • Sometimes a “traditional” plan is best after all • Decision made based on query optimizer’s cost model

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