Wikipedia

Bitmap index

Abitmap indexis a special kind ofdatabase indexthat usesbitmaps.

Bitmap indexes have traditionally been considered to work well forlow-cardinalitycolumns,which have a modest number of distinct values, either absolutely, or relative to the number of records that contain the data. The extreme case of low cardinality isBoolean data(e.g., does a resident in a city have internet access?), which has two values, True and False. Bitmap indexes usebit arrays(commonly called bitmaps) and answer queries by performingbitwise logical operationson these bitmaps. Bitmap indexes have a significant space and performance advantage over other structures for query of such data. Their drawback is they are less efficient than the traditionalB-treeindexes for columns whose data is frequently updated: consequently, they are more often employed in read-only systems that are specialized for fast query - e.g., data warehouses, and generally unsuitable foronline transaction processingapplications.

Some researchers argue that bitmap indexes are also useful for moderate or even high-cardinality data (e.g., unique-valued data) which is accessed in a read-only manner, and queries access multiple bitmap-indexed columns using theAND,ORorXORoperators extensively.[1]

Bitmap indexes are also useful indata warehousingapplications for joining a largefact tableto smallerdimension tablessuch as those arranged in astar schema.

Example

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Continuing the internet access example, a bitmap index may be logically viewed as follows:

Identifier HasInternet Bitmaps
Y N
1 Yes 1 0
2 No 0 1
3 No 0 1
4 Unspecified 0 0
5 Yes 1 0

On the left,Identifierrefers to the unique number assigned to each resident, HasInternet is the data to be indexed, the content of the bitmap index is shown as two columns under the headingbitmaps.Each column in the left illustration under the Bitmaps header is abitmapin the bitmap index. In this case, there are two such bitmaps, one for "has internet"Yesand one for "has internet"No.It is easy to see that each bit in bitmapYshows whether a particular row refers to a person who has internet access. This is the simplest form of bitmap index. Most columns will have more distinct values. For example, the sales amount is likely to have a much larger number of distinct values. Variations on the bitmap index can effectively index this data as well. We briefly review three such variations.

Note: Many of the references cited here are reviewed at (John Wu (2007)).[2]For those who might be interested in experimenting with some of the ideas mentioned here, many of them are implemented in open source software such as FastBit,[3]the Lemur Bitmap Index C++ Library,[4]the Roaring Bitmap Java library[5]and theApache HiveData Warehouse system.

Compression

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For historical reasons, bitmap compression andinverted list compressionwere developed as separate lines of research, and only later were recognized as solving essentially the same problem.[6]

Software cancompresseach bitmap in a bitmap index to save space. There has been considerable amount of work on this subject.[7][8] Though there are exceptions such as Roaring bitmaps,[9]Bitmap compression algorithms typically employrun-length encoding,such as the Byte-aligned Bitmap Code,[10]the Word-Aligned Hybrid code,[11]the Partitioned Word-Aligned Hybrid (PWAH) compression,[12]the Position List Word Aligned Hybrid,[13]the Compressed Adaptive Index (COMPAX),[14]Enhanced Word-Aligned Hybrid (EWAH)[15]and the COmpressed 'N' Composable Integer SEt (CONCISE).[16][17]These compression methods require very little effort to compress and decompress. More importantly, bitmaps compressed with BBC, WAH, COMPAX, PLWAH, EWAH and CONCISE can directly participate inbitwise operationswithout decompression. This gives them considerable advantages over generic compression techniques such asLZ77.BBC compression and its derivatives are used in a commercialdatabase management system.BBC is effective in both reducing index sizes and maintainingqueryperformance. BBC encodes the bitmaps inbytes,while WAH encodes in words, better matching currentCPUs."On both synthetic data and real application data, the new word aligned schemes use only 50% more space, but perform logical operations on compressed data 12 times faster than BBC."[18]PLWAH bitmaps were reported to take 50% of the storage space consumed by WAH bitmaps and offer up to 20% faster performance onlogical operations.[13]Similar considerations can be done for CONCISE[17]and Enhanced Word-Aligned Hybrid.[15]

The performance of schemes such as BBC, WAH, PLWAH, EWAH, COMPAX and CONCISE is dependent on the order of the rows. A simple lexicographical sort can divide the index size by 9 and make indexes several times faster.[19]The larger the table, the more important it is to sort the rows. Reshuffling techniques have also been proposed to achieve the same results of sorting when inde xing streaming data.[14]

Encoding

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Basic bitmap indexes use one bitmap for each distinct value. It is possible to reduce the number of bitmaps used by using a differentencodingmethod.[20][21]For example, it is possible to encode C distinct values using log(C) bitmaps withbinary encoding.[22]

This reduces the number of bitmaps, further saving space, but to answer any query, most of the bitmaps have to be accessed. This makes it potentially not as effective as scanning a vertical projection of the base data, also known as amaterialized viewor projection index. Finding the optimal encoding method that balances (arbitrary) query performance, index size and index maintenance remains a challenge.

Without considering compression, Chan and Ioannidis analyzed a class of multi-component encoding methods and came to the conclusion that two-component encoding sits at the kink of the performance vs. index size curve and therefore represents the best trade-off between index size and query performance.[20]

Binning

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For high-cardinality columns, it is useful to bin the values, where each bin covers multiple values and build the bitmaps to represent the values in each bin. This approach reduces the number of bitmaps used regardless of encoding method.[23]However, binned indexes can only answer some queries without examining the base data. For example, if a bin covers the range from 0.1 to 0.2, then when the user asks for all values less than 0.15, all rows that fall in the bin are possible hits and have to be checked to verify whether they are actually less than 0.15. The process of checking the base data is known as the candidate check. In most cases, the time used by the candidate check is significantly longer than the time needed to work with the bitmap index. Therefore, binned indexes exhibit irregular performance. They can be very fast for some queries, but much slower if the query does not exactly match a bin.

History

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The concept of bitmap index was first introduced by Professor Israel Spiegler and Rafi Maayan in their research "Storage and Retrieval Considerations of Binary Data Bases", published in 1985.[24]The first commercial database product to implement a bitmap index was Computer Corporation of America'sModel 204.Patrick O'Neilpublished a paper about this implementation in 1987.[25]This implementation is a hybrid between the basic bitmap index (without compression) and the list of Row Identifiers (RID-list). Overall, the index is organized as aB+tree.When the column cardinality is low, each leaf node of the B-tree would contain long list of RIDs. In this case, it requires less space to represent the RID-lists as bitmaps. Since each bitmap represents one distinct value, this is the basic bitmap index. As the column cardinality increases, each bitmap becomes sparse and it may take more disk space to store the bitmaps than to store the same content as RID-lists. In this case, it switches to use the RID-lists, which makes it aB+treeindex.[26][27]

In-memory bitmaps

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One of the strongest reasons for using bitmap indexes is that the intermediate results produced from them are also bitmaps and can be efficiently reused in further operations to answer more complex queries. Many programming languages support this as a bit array data structure. For example, Java has theBitSetclass.

Some database systems that do not offer persistent bitmap indexes use bitmaps internally to speed up query processing. For example,PostgreSQLversions 8.1 and later implement a "bitmap index scan" optimization to speed up arbitrarily complexlogical operationsbetween available indexes on a single table.

For tables with many columns, the total number of distinct indexes to satisfy all possible queries (with equality filtering conditions on either of the fields) grows very fast, being defined by this formula:

.[28][29]

A bitmap index scan combines expressions on different indexes, thus requiring only one index per column to support all possible queries on a table.

Applying this access strategy to B-tree indexes can also combine range queries on multiple columns. In this approach, a temporary in-memory bitmap is created with onebitfor each row in the table (1MBcan thus store over 8 million entries). Next, the results from each index are combined into the bitmap usingbitwise operations.After all conditions are evaluated, the bitmap contains a "1" for rows that matched the expression. Finally, the bitmap is traversed and matching rows are retrieved. In addition to efficiently combining indexes, this also improveslocality of referenceof table accesses, because all rows are fetched sequentially from the main table.[30]The internal bitmap is discarded after the query. If there are too many rows in the table to use 1 bit per row, a "lossy" bitmap is created instead, with a single bit per disk page. In this case, the bitmap is just used to determine which pages to fetch; the filter criteria are then applied to all rows in matching pages.

References

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Notes
  1. ^Bitmap Index vs. B-tree Index: Which and When?,Vivek Sharma, Oracle Technical Network.
  2. ^John Wu (2007)."Annotated References on Bitmap Index".Archived fromthe originalon 2012-06-30.
  3. ^FastBit
  4. ^Lemur Bitmap Index C++ Library
  5. ^Roaring bitmaps
  6. ^Jianguo Wang; Chunbin Lin; Yannis Papakonstantinou; Steven Swanson. "An Experimental Study of Bitmap Compression vs. Inverted List Compression"Archived2019-12-07 at theWayback Machine. 2017. doi: 10.1145/3035918.3064007
  7. ^T. Johnson (1999)."Performance Measurements of Compressed Bitmap Indices"(PDF).In Malcolm P. Atkinson;Maria E. Orlowska;Patrick Valduriez; Stanley B. Zdonik; Michael L. Brodie (eds.).VLDB'99, Proceedings of 25th International Conference on Very Large Data Bases, September 7–10, 1999, Edinburgh, Scotland, UK.Morgan Kaufmann. pp. 278–89.ISBN978-1-55860-615-9.
  8. ^Wu K, Otoo E, Shoshani A (March 5, 2004)."On the performance of bitmap indices for high cardinality attributes"(PDF).
  9. ^Chambi, S.; Lemire, D.; Kaser, O.; Godin, R. (2016). "Better bitmap performance with Roaring bitmaps".Software: Practice and Experience.46(5): 709–719.arXiv:1402.6407.doi:10.1002/spe.2325.S2CID1139669.
  10. ^Byte aligned data compression
  11. ^Word aligned bitmap compression method, data structure, and apparatus
  12. ^van Schaik, Sebastiaan; de Moor, Oege (2011)."A memory efficient reachability data structure through bit vector compression".Proceedings of the 2011 international conference on Management of data.SIGMOD '11. Athens, Greece: ACM. pp. 913–924.doi:10.1145/1989323.1989419.ISBN978-1-4503-0661-4.
  13. ^abDeliège F, Pedersen TB (2010)."Position list word aligned hybrid: optimizing space and performance for compressed bitmaps"(PDF).In Ioana Manolescu, Stefano Spaccapietra, Jens Teubner, Masaru Kitsuregawa, Alain Leger, Felix Naumann, Anastasia Ailamaki, Fatma Ozcan (eds.).EDBT '10, Proceedings of the 13th International Conference on Extending Database Technology.New York, NY, USA: ACM. pp. 228–39.doi:10.1145/1739041.1739071.ISBN978-1-60558-945-9.S2CID12234453.
  14. ^abF. Fusco; M. Stoecklin; M. Vlachos (September 2010)."NET-FLi: on-the-fly compression, archiving and inde xing of streaming network traffic"(PDF).Proc. VLDB Endow.3(1–2): 1382–93.doi:10.14778/1920841.1921011.S2CID787443.
  15. ^abLemire, D.; Kaser, O.; Aouiche, K. (2010). "Sorting improves word-aligned bitmap indexes".Data & Knowledge Engineering.69:3–28.arXiv:0901.3751.doi:10.1016/j.datak.2009.08.006.S2CID6297890.
  16. ^Concise: Compressed 'n' Composable Integer SetArchivedMay 28, 2011, at theWayback Machine
  17. ^abColantonio A, Di Pietro R (31 July 2010)."Concise: Compressed 'n' Composable Integer Set"(PDF).Information Processing Letters.110(16): 644–50.arXiv:1004.0403.doi:10.1016/j.ipl.2010.05.018.S2CID8092695.Archived fromthe original(PDF)on 22 July 2011.Retrieved2 February2011.
  18. ^Wu K, Otoo EJ, Shoshani A (2001)."A Performance comparison of bitmap indexes"(PDF).In Henrique Paques,Ling Liu,David Grossman (eds.).CIKM '01 Proceedings of the tenth international conference on Information and knowledge management.New York, NY, USA: ACM. pp. 559–61.doi:10.1145/502585.502689.ISBN978-1-58113-436-0.S2CID10974671.
  19. ^D. Lemire; O. Kaser; K. Aouiche (January 2010). "Sorting improves word-aligned bitmap indexes".Data & Knowledge Engineering.69(1): 3–28.arXiv:0901.3751.doi:10.1016/j.datak.2009.08.006.S2CID6297890.
  20. ^abC.-Y. Chan; Y. E. Ioannidis (1998)."Bitmap index design and evaluation"(PDF).In Ashutosh Tiwary; Michael Franklin (eds.).Proceedings of the 1998 ACM SIGMOD international conference on Management of data (SIGMOD '98).New York, NY, USA: ACM. pp. 355–6.doi:10.1145/276304.276336.ISBN0897919955.
  21. ^C.-Y. Chan; Y. E. Ioannidis (1999)."An efficient bitmap encoding scheme for selection queries"(PDF).Proceedings of the 1999 ACM SIGMOD international conference on Management of data (SIGMOD '99).New York, NY, USA: ACM. pp. 215–26.doi:10.1145/304182.304201.ISBN1581130848.
  22. ^P. E. O'Neil; D. Quass (1997). "Improved Query Performance with Variant Indexes". In Joan M. Peckman; Sudha Ram; Michael Franklin (eds.).Proceedings of the 1997 ACM SIGMOD international conference on Management of data (SIGMOD '97).New York, NY, USA: ACM. pp. 38–49.doi:10.1145/253260.253268.ISBN0897919114.
  23. ^N. Koudas (2000). "Space efficient bitmap inde xing".Proceedings of the ninth international conference on Information and knowledge management (CIKM '00).New York, NY, USA: ACM. pp. 194–201.doi:10.1145/354756.354819.ISBN978-1581133202.S2CID7504216.
  24. ^Spiegler I; Maayan R (1985). "Storage and retrieval considerations of binary data bases".Information Processing and Management.21(3): 233–54.doi:10.1016/0306-4573(85)90108-6.
  25. ^O'Neil, Patrick (1987). "Model 204 Architecture and Performance". In Dieter Gawlick; Mark N. Haynie; Andreas Reuter (eds.).Proceedings of the 2nd International Workshop on High Performance Transaction Systems.London, UK: Springer-Verlag. pp. 40–59.
  26. ^D. Rinfret; P. O'Neil; E. O'Neil (2001). "Bit-sliced index arithmetic". In Timos Sellis (ed.).Proceedings of the 2001 ACM SIGMOD international conference on Management of data (SIGMOD '01).New York, NY, USA: ACM. pp. 47–57.doi:10.1145/375663.375669.ISBN1581133324.
  27. ^E. O'Neil; P. O'Neil; K. Wu (2007)."Bitmap Index Design Choices and Their Performance Implications"(PDF).11th International Database Engineering and Applications Symposium (IDEAS 2007).pp. 72–84.doi:10.1109/IDEAS.2007.19.ISBN978-0-7695-2947-9.
  28. ^Alex Bolenok (2009-05-09)."Creating indexes".
  29. ^Egor Timoshenko."On minimal collections of indexes"(PDF).
  30. ^Tom Lane (2005-12-26)."Re: Bitmap indexes etc".PostgreSQL mailing lists.Retrieved2007-04-06.
Bibliography
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