Cache Conscious Indexing for DecisionSupport in Main Memory

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Cache Conscious Indexing for Decision-Support in
Main Memory

• Pradip Dhara

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Why In-memory databases

• Telecommunications
• CAD tools
• Moores law will allow us to store relations in
  memory

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Redesigning DBMSs

• Optimize memory-cpu performance vs disk-memory
  performance
• Re-evaluate space/time tradeoff space isnt
  cheap
• Given certain space requirement, need to optimize
  response time for lookups

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Indices in In-Memory DBMSs

• Little extra space vs. Increased performance
• Index design takes on new dimensions when looking
  at in-memory databases
• Space overhead can not be ignored hash tables
  are unacceptable

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Hardware solutions

• Caches
• Growing disparity between CPU performance and
  memory performance.
• Cache misses cant be overlapped

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Solution

• CSS-trees indices exploit cache behavior to get
  improved performance

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Direct Mapped Cache
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Fully Associative Cache
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2-Way Set Associative Cache
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Binary Search on Sorted Array

• Store the relation in sorted order on a key
• Cache performance dependent upon tuple size

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T-trees

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Enhanced B trees

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Hash Indices

000

001
010
011
Put however many pairs fit into a
cache line
100
101
110
111
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Idea Behind CSS-trees

• Save space by not storing pointers
• Use an array as a tree
• Implicitly store pointers as offsets into the
  array

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Useful Formulas for CSS-trees

n of elements m of elements per node N
of nodes
Children of a node b are nodes b(m1) to b(m1)
(m1)
(EQ 1)
N n m
(EQ 2)
of Internal Nodes
(EQ 3)
First leaf node in bottom level
(EQ 4)
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How it works

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Building a full CSS-tree

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Searching Within a Node

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Level CSS-trees

m 2t
Entries per node m -1
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Level vs. Full CSS-trees

• Level CSS-trees will be deeper due to the
  difference in branching factor
• Level CSS-trees have fewer comparisons per node
• Level CSS-trees have more cache accesses and and
  node traversals
  

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Time Analysis

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Space Analysis

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Experiment

• Results are for Ultra Sparc II
• Keys randomly generated integers between 0 and 1
  million
• Performed 5 tests of 100,00 searches for random
  keys

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Figure 5a Array Size vs. time

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Figure 5b Array Size vs. Time

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Figure 6a Array Size vs. 2nd cache accesses

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Figure 6b Array Size vs. 2nd cache misses

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Figure 7 Node Size vs. Time

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CSS Performance on Other Queries

• CSS is very good for individual selection queries
• CSS will probably perform the best in range
  queries
• Index nested loops join vs. Sort merge join

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Doubts About CSS

• Flexibility of CSS-trees across different cache
  designs
• Any applicability to variable sized records
• Multiple CSS-tree indices on different keys

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Conclusion

• CSS-trees improve searching performance by
  exploiting cache consciousness.

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One Last Thought

• Cache designs
• Should we redesign them to let programmers have
  control?