1. C-Store: Data Model and Data Organization Jianlin Feng School of Software SUN YAT-SEN UNIVERSITY May 17, 2010

2. Data Model: standard relational model A database:  A set of named relations (tables) A relation  A set of named attributes (columns) Primary key  A set of attributes whose values uniquely identify a row (tuple) in a relation. Foreign key  References a primary key in another relation.

3. Primary Keys and Foreign Keys

4. How to Implement a logical relation? Given a logical relation R Row Store  R has a direct physical correspondence. Column Store (C-Store)  R may not have a direct physical correspondence.  Covered by a set of C-Store Projections.

5. C-Store Projection Is anchored on a given logical table T. Contains one or more attributes from T. Can also contain any number of attributes from other tables.  Attributes from other tables must be referenced by a sequence of n:1 (i.e., foreign keys) relationships from T.

6. How to Construct a Projection? Given a logical table T Extract the attributes of interest from T.  Retain any duplicate rows  In standard Projection, duplicates are deleted. Obtain the attributes of interest from other tables  Perform foreign-key joins.

7. Attribute from DEPT table

8. Sort Key Tuples in a projection are stored column-wise.  K attributes  K columns  Each column is sorted on the same Sort Key. Sort Key  Can be any column or columns in a projection

9. Examples of Sort Key

10. Each Projection is horizontall y partitioned into Segments

11. Horizontal Partition of a Projection Each projection is horizontally partitioned into 1 or more segments. SID > 0, Segment identifier Value-based partitioning on the Sort Key of a projection  Each segment has a key range of the sort key.  The set of all key ranges partitions the whole space of sort key.

12. How to Re-construct a Complete Tuple? To answer any SQL query  There must be a covering set of projections for every logical table T. Every column in T is stored in at least one projection. To re-construct a tuple, Join segments from different projections  Using Storage Keys and Join Indexes

13. Storage Keys A segment, horizontal fragment of a projection  May involve several coulmns  Associate every data value of each column with a Storage Key, SK.  In the same segment, data values from different columns with matching SK belong to the same logical tuple. A SK is simply the ID of a logical tuple.

14. Architecture of C-Store (Vertica) On a Single Node

15. Storage Keys in Read Store (RS) SKs are numbered 1,2,3,... SKs are not physically stored  But are inferred from a tuple’s physical position in a column. Why SKs can be inferred?  All the columns in the same segment are sorted on the same Sort Key.

16. Storage Keys in Write Store (WS) SKs are physically stored SKs are represented as integers. Each SK in WS is larger than the largest SK for any segment in RS.

17. join indexes: A Mapping Table Suppose T1 and T2 are two projections that cover a logical table T. For each segment of T1, build a join index to T2  is a Table with rows : (s: SID in T2, k: Storage Key in Segment s)

19. Ordering of Data in Each Column Self-order  the column is ordered by values in itself. Foreign-order  the column is ordered by values in other column in the same projection. A projection may involve several columns Example  Projection EMP1(name, age| age)  Column age is Self-order  Column name is foreign order

20. Column Type in Read Store(RS) Type 1: Self-order, few distinct values Type 2: Foreign-order, few distinct values Type 3: Self-order, many distinct values Type 4: Foreign-order, many distinct values

21. Compression of Columns in Type 1: Self-order, few distinct values Represented by a sequence of triples (v, f, n) v: a data value stored in the column f : the position in the column where v first appears. n: the number of times v appears in the column Example: 4’s appear in positions 12-18, is recorded as (4, 12, 7) One triple is required for each distinct value in the column.

22. Fast Search over Columns in Type 1 Using Clustered B-Tree (i.e., Primary B-Tree) Densepack the B-Tree  No on-line updates in RS Using large disk blocks  64-128K  The height of this index can be kept small (2 or less)

23. Compression of Columns in Type 2: Foreign-order, few distinct values Represented by a sequence of tuples (v, b) v: a data value stored in the column b: a bitmap indicating the positions in which v is stored. Use Run-Length Encoding to compress bitmaps. Column C1 V=0V=1V=2 0100 0100 1010 1010 2001 1010 0100 2001 1010

24. Fast Search over Columns in Type 2 To efficiently find the i-th value in a column, Use Offset indexes  B-Trees that map positions in a column to the values contained in that column.

25. Compression of Columns in Type 3: Self-order, many distinct values Basic Idea  Represent each value in the column as a delta from the previous value. Use block (64-128K) as the unit of compression. Like compressing an Inverted Index Column C1Delta representation 11 (starting value) 43 73 (delta) 70 (delta) 81 (delta) 124 (delta)

26. Fast Search over Columns in Type 3 Use densepacked B-Tree at the block-level  A block is viewed as a tuple.

27. Compression of Columns in Type 4: Foreign-order, many distinct values Two choices at the moment  Do not compress  Use densepacked B-Tree Open for further research

28. Write Store (WS) WS is also a Column Store  To avoid writing two query optimizers Implements the identical physical DBMS design as RS. The Major Difference due to Updates in WS  Storage representation

29. How to Do Updates? Update  Insert a new tuple  Modify an existing tuple  Delete an (existing) tuple Update depends on first doing a query  Insert: need to check Primary Key Constraint etc.  Modify: need to first find the specified tuple  Delete: need to first find the specified tuple

30. Queries in C-Store Use some known values of some columns as conditions to search values on other columns  Example table: EMP1(name, age| age)  Example query: use age values to query name values. Tuples in C-Store are stored column-wise  We need to keep track of all column values of the same logical tuple  The Idea: Storage Key as the tuple ID.

31. How to Speed-up Queries in C-Store? The Basic Idea:  Pre-sort every projection in some SORT KEY order  Keep several copies of the same projection, each copy is pre-sorted in different sort key order.  For a given query, use a copy of the projection whose order matches with the query conditions. Therefore queries in C-Store usually equal to searches via sort key. Note:Each Projection in WS has only one copy

32. Storage Key in WS The Storage Key, SK, for each tuple is explicitly stored in each WS segment.  Columns in WS only keep a logical SORT KEY order via SKs.  Delay physical sorts on SORT KEY order when tuples are moved from WS to RS. A unique SK is given to each insert of a logical tuple r in a table T.  SK is a serial number generated by system.  The SK of r must be recorded in each projection that stores data for r.

33. Storage Representation of Columns in WS Every column in a Projection  Represented as a collection of (v, sk) pairs v : a data value in the column sk : the storage key (explicitly stored) Build a B-Tree over each column  Use the second field of each pair, sk, as the KEY

34. Sort Keys of Each Projection in WS Represented as a collection of (s, sk) pairs  s : a sort key value  sk : the storage key describing where s first appears. Build a B-Tree over the (s, sk) pairs  Use the first field of each pair, s, as the KEY

35. Searches via Sort Key: Two Steps 1 st Step,use the B-Tree over the (s, sk) pairs  Search condition: known sort key values  Search result:corresponding storage keys 2 nd Step, use the B-Tree over the each column (i.e., the (v, sk) pairs)  Search condition: storage keys found in 1 st Step.  Search result:data values in the column.

36. Partition of a Projection in WS Partitioning a Projection in the same way as in RS  Equals to partitioning the space of sort key  1:1 mapping between RS segments and WS ones. A tuple is identified by a (sid, storage_key) pair in either RS or WS  sid: segment ID  Storage_key: the SK of the tuple

37. General Picture of WS Usually is very small, can be fully stored in Memory  Data processing is fast in memory Do not compress data, represent data directly Each projection uses B-Tree indexing to maintain a logical sort-key order.  The B-Trees are secondary B-Tree.

38. References 1. Mike Stonebraker, Daniel Abadi, Adam Batkin, Xuedong Chen, Mitch Cherniack, Miguel Ferreira, Edmond Lau, Amerson Lin, Sam Madden, Elizabeth O'Neil, Pat O'Neil, Alex Rasin, Nga Tran and Stan Zdonik. C-Store: A Column Oriented DBMS, VLDB, 2005. (http://db.csail.mit.edu/projects/cstore/vldb.pdf)http://db.csail.mit.edu/projects/cstore/vldb.pdf 2. VERTICA DATABASE TECHNICAL OVERVIEW WHITE PAPER. http://www.vertica.com/php/pdfgateway?file=Vertic aArchitectureWhitePaper.pdf