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Modern BTree techniques DMITRY DOLGOV 31-01-2020 @aspis7 1 @aspis7 1 Graefe, Goetz and Harumi A. Kuno. Modern B- tree techniques. IEEE 27th International Confer- ence on Data Engineering, 2011. D. Comet, Ubiquitous B-tree,

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Modern BTree techniques

DMITRY DOLGOV

31-01-2020

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@aspis7

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@aspis7

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  • D. Comet, ”Ubiquitous B-tree”, ACM Comp. Surv.,
  • vol. 11, no. 2, 1979.

Graefe, Goetz and Harumi A. Kuno. ”Modern B- tree techniques.” IEEE 27th International Confer- ence on Data Engineering, 2011.

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  • D. Comet, ”Ubiquitous B-tree”, ACM Comp. Surv.,
  • vol. 11, no. 2, 1979.

Graefe, Goetz and Harumi A. Kuno. ”Modern B- tree techniques.” IEEE 27th International Confer- ence on Data Engineering, 2011.

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RUM conjecture B-Tree Key normalization & friends SB-Tree MDAM Hybrid, Bw-Tree, DPTree Trie Everything else

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B-Tree B+-Tree Blink-Tree DPTree wB+-Tree NV-Tree FPTree FASTFAIR HiKV Masstree Skip List ART WORT CDDS-Tree Bw-Tree HOT KISS-Tree VAST-Tree FAST HV-Tree UB-Tree LHAM MDAM Hybrid B+-Tree

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Mem Write Read

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Mem Write Read

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Complexity? Mem Write Read

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B+Tree

  • P. Lehman and S. Yao, Efficient Locking for Concurrent Operations on B-Trees, ACM Transactions on Database Systems, Vol 6, No. 4, December

1981, pp 650-670

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B+Tree

  • P. Lehman and S. Yao, Efficient Locking for Concurrent Operations on B-Trees, ACM Transactions on Database Systems, Vol 6, No. 4, December

1981, pp 650-670

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B+Tree

  • P. Lehman and S. Yao, Efficient Locking for Concurrent Operations on B-Trees, ACM Transactions on Database Systems, Vol 6, No. 4, December

1981, pp 650-670

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B+Tree

  • P. Lehman and S. Yao, Efficient Locking for Concurrent Operations on B-Trees, ACM Transactions on Database Systems, Vol 6, No. 4, December

1981, pp 650-670

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B+Tree

  • P. Lehman and S. Yao, Efficient Locking for Concurrent Operations on B-Trees, ACM Transactions on Database Systems, Vol 6, No. 4, December

1981, pp 650-670

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B+Tree

  • P. Lehman and S. Yao, Efficient Locking for Concurrent Operations on B-Trees, ACM Transactions on Database Systems, Vol 6, No. 4, December

1981, pp 650-670

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Page split

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Page split

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Page split

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Page split

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Page merge ”By adding periodic rebuilding of the tree, we

  • btain a data structure that is theoreticaly

superior to standard B-trees in many ways. Our results suggest that rebalancing on deletion no only unnecessary but may be harmful.”

  • S. Sen and R. E. Tarjan, ”Deletion without rebalancing in multiway search trees.” ISAAC, pp.

832-841, 2009

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Mem Write Read B-Tree

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Mem Write Read B-Tree

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Mem Write Read B-Tree

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Key normalization 1 ”Dirk” ”Bart” 1 0..01 1 11..00 ∅ 1 10..10 ∅ 2 ”Todd” Null 1 0..10 1 01..00 ∅ 0 Null ”” Null 0 1 ∅ 0

  • R. C. Singleton, ”An efficient algorithm for sorting with minimal storage”, Communications of the ACM, vol. 12, no.3 pp. 185-186, 1969

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Prefix truncation Smith Jack 01-02-2019 Smith Jane 02-03-2019 Smith James 03-04-2019

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Prefix truncation Smith Ja ck 01-02-2019 Smith Ja ne 02-03-2019 Smith Ja mes 03-04-2019

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Prefix truncation Smith Ja ck 01-02-2019 ne 02-03-2019 mes 03-04-2019

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Prefix truncation

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Prefix truncation

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Dynamic prefix truncation

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Dynamic prefix truncation

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Dynamic prefix truncation

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Suffix truncation Johnson David 04-02-2019 Miller Kevin 01-02-2019 Miller Ned 02-03-2019 Miller Steven 03-04-2019 Smith Jack 01-02-2019

  • R. Bayer, K. Unterauer, ”Prefix B-trees”, ACM Transactions on Database Systems, vol. 2, no. 1, pp. 11-26, 1977

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Suffix truncation Johnson David 04-02-2019 Miller Kevin 01-02-2019 Miller Ned 02-03-2019 Miller Steven 03-04-2019 Smith Jack 01-02-2019

  • R. Bayer, K. Unterauer, ”Prefix B-trees”, ACM Transactions on Database Systems, vol. 2, no. 1, pp. 11-26, 1977

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Suffix truncation Johnson David 04-02-2019 Miller Kevin 01-02-2019 Miller N ed 02-03-2019 Miller Steven 03-04-2019 Smith Jack 01-02-2019

  • R. Bayer, K. Unterauer, ”Prefix B-trees”, ACM Transactions on Database Systems, vol. 2, no. 1, pp. 11-26, 1977

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Suffix truncation J ohnson David 04-02-2019 Miller Kevin 01-02-2019 Miller Ned 02-03-2019 Miller Steven 03-04-2019 Smith Jack 01-02-2019

  • R. Bayer, K. Unterauer, ”Prefix B-trees”, ACM Transactions on Database Systems, vol. 2, no. 1, pp. 11-26, 1977

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Indirection vector

CPU Cache

  • G. Graefe, Per-Ake Larson, ”B-tree indexes and CPU caches”, International Conference on Data Engineering, pp. 349-358, 2001

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Indirection vector

a b c d

CPU Cache

  • G. Graefe, Per-Ake Larson, ”B-tree indexes and CPU caches”, International Conference on Data Engineering, pp. 349-358, 2001

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Indirection vector

a b c d

CPU Cache

  • G. Graefe, Per-Ake Larson, ”B-tree indexes and CPU caches”, International Conference on Data Engineering, pp. 349-358, 2001

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SB-tree

  • P. E. O’Neil, ”The SB-tree: An index-sequential structure for high performance sequential access”, Acta Informatica, vol. 29, no. 3. pp. 241-265, 1992

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SB-tree

  • P. E. O’Neil, ”The SB-tree: An index-sequential structure for high performance sequential access”, Acta Informatica, vol. 29, no. 3. pp. 241-265, 1992

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Multidimentional Access Method

1,a ... 1,z 2,a ... 2,z 3,a ... 3,z

  • H. Leslie, R. Jain, D. Birdsall, H. Yaghmai, ”Efficient search of multidimentionel B-trees”,

ACM Transactions on Database Systems, vol. 6, no. 4, pp. 650-670, 1995

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Multidimentional Access Method

1,a ... 1,z 2,a ... 2,z 3,a ... 3,z

  • H. Leslie, R. Jain, D. Birdsall, H. Yaghmai, ”Efficient search of multidimentionel B-trees”,

ACM Transactions on Database Systems, vol. 6, no. 4, pp. 650-670, 1995

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Multidimentional Access Method

1,a ... 1,z 2,a ... 2,z 3,a ... 3,z

  • H. Leslie, R. Jain, D. Birdsall, H. Yaghmai, ”Efficient search of multidimentionel B-trees”,

ACM Transactions on Database Systems, vol. 6, no. 4, pp. 650-670, 1995

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Multidimentional Access Method

1,a ... 1,z 2,a ... 2,z 3,a ... 3,z

  • H. Leslie, R. Jain, D. Birdsall, H. Yaghmai, ”Efficient search of multidimentionel B-trees”,

ACM Transactions on Database Systems, vol. 6, no. 4, pp. 650-670, 1995

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Partitioned B-tree

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Partitioned B-tree

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Partitioned B-tree

  • G. Graefe, ”Sorting and indexing with partitioned B-Trees”, Classless Inter Domain

Routing, 2003

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Partitioned B-tree

  • G. Graefe, ”Sorting and indexing with partitioned B-Trees”, Classless Inter Domain

Routing, 2003

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Partitioned B-tree

Riegger Christian, Vincon Tobias, Petrov Ilia. (2017). Write-optimized indexing with partitioned b-trees. 296-300.

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Partitioned B-tree

Riegger Christian, Vincon Tobias, Petrov Ilia. (2017). Write-optimized indexing with partitioned b-trees. 296-300.

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Hybrid indexes

Insert

Huanchen Zhang, David G. Andersen, Andrew Pavlo, Michael Kaminsky, Lin Ma, and Rui Shen. 2016. Reducing the Storage Overhead of Main-Memory OLTP Databases with Hybrid Indexes. In Proceedings of the 2016 International Conference on Management of Data (SIGMOD ’16). Association for Computing Machinery, New York, NY, USA, 1567–1581.

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Hybrid indexes

Insert

Huanchen Zhang, David G. Andersen, Andrew Pavlo, Michael Kaminsky, Lin Ma, and Rui Shen. 2016. Reducing the Storage Overhead of Main-Memory OLTP Databases with Hybrid Indexes. In Proceedings of the 2016 International Conference on Management of Data (SIGMOD ’16). Association for Computing Machinery, New York, NY, USA, 1567–1581.

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Hybrid indexes

Insert

Huanchen Zhang, David G. Andersen, Andrew Pavlo, Michael Kaminsky, Lin Ma, and Rui Shen. 2016. Reducing the Storage Overhead of Main-Memory OLTP Databases with Hybrid Indexes. In Proceedings of the 2016 International Conference on Management of Data (SIGMOD ’16). Association for Computing Machinery, New York, NY, USA, 1567–1581.

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Hybrid indexes

Insert

Huanchen Zhang, David G. Andersen, Andrew Pavlo, Michael Kaminsky, Lin Ma, and Rui Shen. 2016. Reducing the Storage Overhead of Main-Memory OLTP Databases with Hybrid Indexes. In Proceedings of the 2016 International Conference on Management of Data (SIGMOD ’16). Association for Computing Machinery, New York, NY, USA, 1567–1581.

19

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Hybrid indexes

Insert Read

Huanchen Zhang, David G. Andersen, Andrew Pavlo, Michael Kaminsky, Lin Ma, and Rui Shen. 2016. Reducing the Storage Overhead of Main-Memory OLTP Databases with Hybrid Indexes. In Proceedings of the 2016 International Conference on Management of Data (SIGMOD ’16). Association for Computing Machinery, New York, NY, USA, 1567–1581.

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Hybrid indexes

Insert Read

Huanchen Zhang, David G. Andersen, Andrew Pavlo, Michael Kaminsky, Lin Ma, and Rui Shen. 2016. Reducing the Storage Overhead of Main-Memory OLTP Databases with Hybrid Indexes. In Proceedings of the 2016 International Conference on Management of Data (SIGMOD ’16). Association for Computing Machinery, New York, NY, USA, 1567–1581.

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Bw-Tree

Levandoski Justin, Lomet David, Sengupta Sudipta. (2012). The Bw-Tree: A B-tree for New Hardware Platforms. Proceedings - International Conference on Data Engineering.

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Bw-Tree

1 2

ID PTR 1 0x... 2 0x...

Levandoski Justin, Lomet David, Sengupta Sudipta. (2012). The Bw-Tree: A B-tree for New Hardware Platforms. Proceedings - International Conference on Data Engineering.

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Bw-Tree

ID PTR 1 0x... 2 0x...

∆ Page

Levandoski Justin, Lomet David, Sengupta Sudipta. (2012). The Bw-Tree: A B-tree for New Hardware Platforms. Proceedings - International Conference on Data Engineering.

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Bw-Tree

ID PTR 1 0x... 2 0x...

∆ Page

Levandoski Justin, Lomet David, Sengupta Sudipta. (2012). The Bw-Tree: A B-tree for New Hardware Platforms. Proceedings - International Conference on Data Engineering.

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Bw-Tree

ID PTR 1 0x... 2 0x...

∆ Page

CAS

Levandoski Justin, Lomet David, Sengupta Sudipta. (2012). The Bw-Tree: A B-tree for New Hardware Platforms. Proceedings - International Conference on Data Engineering.

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Bw-Tree

ID PTR 1 0x... 2 0x...

∆1 ∆2 ∆3 Page

Levandoski Justin, Lomet David, Sengupta Sudipta. (2012). The Bw-Tree: A B-tree for New Hardware Platforms. Proceedings - International Conference on Data Engineering.

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Bw-Tree

ID PTR 1 0x... 2 0x...

∆1 ∆2 ∆3 Page Merged Page

Levandoski Justin, Lomet David, Sengupta Sudipta. (2012). The Bw-Tree: A B-tree for New Hardware Platforms. Proceedings - International Conference on Data Engineering.

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Bw-Tree

ID PTR 1 0x... 2 0x...

∆1 ∆2 ∆3 Page

CAS

Merged Page

Levandoski Justin, Lomet David, Sengupta Sudipta. (2012). The Bw-Tree: A B-tree for New Hardware Platforms. Proceedings - International Conference on Data Engineering.

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DPTree

Insert Read

Zhou Xinjing, Shou Lidan, Chen Ke, Hu Wei, Chen Gang. (2019). DPTree: differential indexing for persistent memory. Proceedings of the VLDB Endowment.

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DPTree

Insert Read

Zhou Xinjing, Shou Lidan, Chen Ke, Hu Wei, Chen Gang. (2019). DPTree: differential indexing for persistent memory. Proceedings of the VLDB Endowment.

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DPTree

Insert Read

Zhou Xinjing, Shou Lidan, Chen Ke, Hu Wei, Chen Gang. (2019). DPTree: differential indexing for persistent memory. Proceedings of the VLDB Endowment.

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DPTree

Insert Read Read Merge

Zhou Xinjing, Shou Lidan, Chen Ke, Hu Wei, Chen Gang. (2019). DPTree: differential indexing for persistent memory. Proceedings of the VLDB Endowment.

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Trie

1 01 1

10

11

0010

1

010

1

011

1

1111

00 00

001100

01

111001

1

11101 0011000

1

0011001

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Trie

1 01 1

10

11

0010

1

010

1

011

1

1111

00 00

001100

01

111001

1

11101 0011000

1

0011001 Leis V., Kemper Alfons, Neumann Thomas. (2013). The adaptive radix tree: ARTful indexing for main-memory databases. Proceedings - International Conference on Data Engineering. 38-49.

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Trie

1 01 1

10

11

0010

1

010

1

011

1

1111

00 00

001100 0011000

1

0011001

01

111001

1

11101 Binna Robert, Zangerle Eva, Pichl Martin, Specht Guenther, Leis Viktor. (2018). HOT: A Height Optimized Trie Index for Main-Memory Database Systems. 521-534.

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Is that all?

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@Unzucht

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Buffered (Lazy) B-Tree Cache conscious B-Tree Learned indexes UB-Tree Skip List LSM Tree ...

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Buffered (Lazy) B-Tree Cache conscious B-Tree Learned indexes UB-Tree Skip List LSM Tree ...

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Buffered (Lazy) B-Tree Cache conscious B-Tree Learned indexes UB-Tree Skip List LSM Tree ...

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Buffered (Lazy) B-Tree Cache conscious B-Tree Learned indexes UB-Tree Skip List LSM Tree ...

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Buffered (Lazy) B-Tree Cache conscious B-Tree Learned indexes UB-Tree Skip List LSM Tree ...

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Buffered (Lazy) B-Tree Cache conscious B-Tree Learned indexes UB-Tree Skip List LSM Tree ...

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Buffered (Lazy) B-Tree Cache conscious B-Tree Learned indexes UB-Tree Skip List LSM Tree ...

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Questions?

 @erthalion  dmitrii.dolgov at zalando dot de  9erthalion6 at gmail dot com

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