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Making B+-Trees Cache Conscious in Main Memory

Making B+-Trees Cache Conscious in Main Memory. Author:Jun Rao, Kenneth A. Ross. Members: Iris Zhang , Grace Yung, Kara Kwon, Jessica Wong. Outline. 1. Introduction 2. Related Work 3. Cache Sensitive B+-Trees 4. Conclusion. Motivation. Significant portion of execution time:

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Making B+-Trees Cache Conscious in Main Memory

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  1. Making B+-Trees Cache Conscious in Main Memory Author:Jun Rao, Kenneth A. Ross Members: Iris Zhang, Grace Yung, Kara Kwon, Jessica Wong

  2. Outline 1. Introduction 2. Related Work 3. Cache Sensitive B+-Trees 4. Conclusion

  3. Motivation • Significant portion of execution time: • second level data cache misses • first level instruction cache misses System Hierarchy

  4. Motivation (Cont’d) 2. CPU speeds have been increasing at a much faster rate than memory speeds • Conclusion: improving cache behavior is going to be an imperative task in main memory data processing • Resolution: using memory index structure

  5. Cache Memories Cache memories are small fast static RAM memories that improve performance by holding recently referenced data. • Parameter: • Capacity • Block Size (cache line) • Associativity • Memory reference: • Hit • Miss

  6. Cache Optimization on Index Structures—B+-Trees • Height-balanced tree • Minimum 50% occupancy (except for root). Each node contains d<= m <= 2d entries. The parameter d is called the order of the tree. (n=2d) • Each node is 1 cache line (cache-line based) • Full pointer B+-Tree (n =2)

  7. Cache Optimization on Index Structures—CSS-Trees • Similar as B+-tree • Eliminating child pointers • Storing child nodes in a fixed sized array. • Nodes are numbered & stored level by level, left to right. • Position of child node can be calculated via arithmetic. • No pointer CSS-Tree

  8. Comparison between B+-Trees and CSS-Trees • Cache Line Size=12 bytes, Key Size=Pointer Size=4 bytes • Search key =3 • B+-Tree CSS-Tree

  9. B+ tree full pointer more cache access and more cache misses efficient for updating operation, e.g. insertion and deletion CSS tree no pointer fewer cache access and fewer cache misses acceptable for static data updated in batches Comparison between B+-Trees and CSS-Trees(cont’d) Conclusion: partial pointer elimination

  10. Cache Sensitive B+-Trees • Cache Sensitive B+-Trees with One Child Pointer • Segmented CSB+-Trees • Full CSB+-Trees

  11. Cache Sensitive B+-Trees with One Pointer • Similar as B+-tree • All the child nodes of any given node are put into a node group with one pointer • Nodes within a node group are stored continuously and can be accessed using an offset to the first node in the group

  12. Cache Sensitive B+-Trees with One Pointer (cont’d) • Cache misses are reduced because a cache line can hold more keys than B+-Trees and can satisfy one more level comparison. • CSB+-Tree can support incremental updates in a way similar to B+-Tree Cache Line Size=64 bytes, Key Size=Pointer Size=4 bytes B+-Tree: 7 keys per node CSB+-Tree: 14 keys per node

  13. 22| 7| 30| 3| 13|19 25| 33| 2|3 5|7 12|13 16|19 20|22 24|25 27|30 31|33 36|39 Operations on CSB+-Tree—Bulkload

  14. Operations on CSB+-Tree— Insertion • Search the leaf node n to insert the new entry • If n is not full, insert the new entry in the appropriate place • Otherwise, split n. Let p be n’ parent node, f be the first-child pointer in p and g be the node-group pointed by f • If p is not full, copy g to g' in which n is split in two nodes. Let f point to g' • If p is full, copy half g to g'. Let f point tog'. Split the node-group of p according to step a

  15. 7| 30| 3| 13|19 25| 33| Operations on CSB+-Tree— Insertion (cont’d) 22| key = 34 2|3 5|7 12|13 16|19 20|22 24|25 27|30 31|33 36|39 a CSB+-Tree of Order 1

  16. 7| 30| 3| 13|19 Operations on CSB+-Tree— Insertion (cont’d) 22| key = 34 25| 33|36 2|3 5|7 12|13 16|19 20|22 24|25 27|30 31|33 34|36 39|

  17. Operations on CSB+-Tree—Search • Determine the rightmost key K in the node that is smaller than the search key • Get the address of the child node • Goto first step until find the search key or there is no other node can be checked • Search method in a node • basic approach uniform approach variable approach

  18. Segmented Cache Sensitive B+-Trees • Problem: it’s time consuming to split a node group • Resolution:SCSB+-Tree • method: divide node group into two segments with one child pointer per segment • result: better split performance, but worse search

  19. Full CSB+-Tree • Motivation: reduce the split cost • Method: • pre-allocate space for a full node group • shift part of the node group along by one node when a node split • Result: • reduce the split cost, but increase the space complexity

  20. Conclusion • CSB+-Trees are more cache conscious than B+-Tree because of partial pointer elimination • CSB+-Trees support efficient incremental updates, but CSS-Trees do not • Partial pointer elimination is a general technique which can be applied to other memory structures

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