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Multidimensional & Bitmap Indexes

Learn how Multidimensional Bitmap Indexes support complex queries in n-dimensional spaces. Explore examples like Grid Files, BV-Trees, and managing Bitmap Indexes efficiently. Study applications in geographical information systems, data warehouses, and data cubes.

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Multidimensional & Bitmap Indexes

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  1. Multidimensional & Bitmap Indexes Section 14.2 and 14.4 ICS 541: MD-BM-Indexes

  2. Lecture outline • Multidimensional Data • Grid Files • Bitmap Indexes • Summary • Reading List ICS 541: MD-BM-Indexes

  3. - Multidimensional Data • Visualizing data as stored in n dimensional space • Support queries that are not common in SQL • Applications: • Geographical information system • Data warehouse • Data cubes • Multidimensional queries • Examples: • Grid file • BANG file • BV-Trees ICS 541: MD-BM-Indexes

  4. - Grid files Emp (55,80) Salary 100000 75000 50000 25000 0 Age 0 25 50 75 100 ICS 541: MD-BM-Indexes

  5. -- Insertion Emp Salary 100000 75000 INSERT INTO Emp VALUES(60,70000); 50000 25000 0 Age 0 25 50 75 100 ICS 541: MD-BM-Indexes

  6. -- Exact Match Query Emp Salary 100000 75000 SELECT * FROM Emp Where age = 60 AND salary = 40000 50000 25000 0 Age 0 25 50 75 100 ICS 541: MD-BM-Indexes

  7. -- Partial Match Query Emp Salary 100000 75000 SELECT * FROM Emp Where age = 60 50000 25000 0 Age 0 25 50 75 100 ICS 541: MD-BM-Indexes

  8. -- Range Query Emp Salary 100000 75000 SELECT * FROM Emp Where age < 60 AND age > 30 50000 25000 0 Age 0 25 50 75 100 ICS 541: MD-BM-Indexes

  9. - Bitmap Indexes • What is Bitmap Index • Motivation for Bitmap Indexes • Compressed Bitmaps • Managing Bitmap Indexes • Summary • Reading List ICS 541: MD-BM-Indexes

  10. -- What is Bitmap Index • A bitmap index for attribute A of relation R is: • A collection of bit-vectors • The number of bit-vectors = the number of distinct values of A in R. • The length of each bit-vector = the cardinality of R. • The bit-vector for value v has 1 in position i, if the ith record has v in attribute A, and it has 0 there if not. • Records are allocated permanent numbers • There is a mapping between record numbers and record addresses. ICS 541: MD-BM-Indexes

  11. -- Example • Assume relation R with • 2 attributes A and B. • Attribute A is of type Integer and B is of type String. • 6 records, numbered 1 through 6 as follows: A, B • 30, foo • 30, bar • 40, baz • 50, foo • 40, bar • 30, baz • A bit map for attribute B is: ICS 541: MD-BM-Indexes

  12. -- Motivation for Bitmap Indexes • Very efficient when used for partial match queries. • The offer the advantage of buckets • Where we find tuples with specified in several attributes without first retrieving all the record that matched in each of the attributes. • They can also help answer range queries ICS 541: MD-BM-Indexes

  13. -- Compressed Bitmaps • Assume: • The number of records in R are n • Attribute A has m distinct values in R • The size of a bitmap index on attribute A is m*n. • If m is large, then the number of 1’s will be around 1/m. • Opportunity to encode • A common encoding approach is called run-length encoding. ICS 541: MD-BM-Indexes

  14. --- Run-length encoding • Represents runs • A run is a sequence of i0’s followed by a 1, by some suitable binary encoding of the integer i. • A run of i 0’s followed by a 1 is encoded by: • First computing how many bits are needed to represent i, Say j • Then represent the run by j-11’s and a single 0 followed by j bits which represent i in binary. • The encoding for i = 1 is 01. j = 1 • The encoding for i = 0 is 00. j = 1 • We concatenate the codes for each run together, and the sequence of bits is the encoding of the entire bit-vector ICS 541: MD-BM-Indexes

  15. --- Run-length Encoding: Example • Let us decode the sequence 11101101001011 • Staring at the beginning (left most bit): • First run: The first 0 is at position 4, so • j = 4, • i = 13 • Second run: 001011 • j = 1 • i = 0 • Last run: 1011 • J = 1 • I = 3 • Our entire run length is thus 13,0,3, hence our bit-vector is: 0000000000000110001 ICS 541: MD-BM-Indexes

  16. -- Managing Bitmap Indexes … • Finding bit vectors • Create secondary key with the attribute value as a search key • Btree • Hash • Finding records • Create secondary key with the record number as a search key. ICS 541: MD-BM-Indexes

  17. … -- Managing Bitmap Indexes • Handling modification • Assume record numbers are not changed • Deletion • Tombstone replaces deleted record • Corresponding bit is set to 0 • Insertion • Record assigned the next record number. • A bit of value 0 or 1 is appended to each bit vector • If new record contains a new value of the attribute, add one bit-vector. • Modification • Change the bit corresponding to the old value of the modified record to 0 • Change the bit corresponding to the new value of the modified record to 1 • If the new value is a new value of A, then insert a new bit-vector. ICS 541: MD-BM-Indexes

  18. - Summary • Multidimensional Data • Grid Files • Insertion • Different kinds of queries • Bitmap Index • Compression • Management ICS 541: MD-BM-Indexes

  19. - Reading List • Section 14.2 and 14.4 of GUW ICS 541: MD-BM-Indexes

  20. END ICS 541: MD-BM-Indexes

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