Chris Olston

1
Offering a Precision-Performance Tradeoff for
Aggregation Queries over Replicated Data

• Chris Olston
• Jennifer Widom

Stanford University
2
Replication Alternatives
performance
precision
3
Replication Alternative 1
Exact Cache
5
3
5
3
Source (fresh)
Source (fresh)
4
Replication Alternative 1
Exact Cache
5 8
3 4
Propagate all updates
5 8
3 4
Source (fresh)
Source (fresh)
5
Replication Alternative 1
Exact Cache
performance
AVG 6
5 8
3 4
exact cache
precision
Propagate all updates
5 8
3 4
Source (fresh)
Source (fresh)
6
Replication Alternative 2
Stale Cache
5
3
Periodic refresh
5 8
3 4
Source (fresh)
Source (fresh)
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Replication Alternative 2
stale cache
Stale Cache
performance
5
3
AVG 4
precision
Periodic refresh
5 8
3 4
Source (fresh)
Source (fresh)
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TRAPP Replication
Bounded Cache
4, 7
2, 4
5
3
Source (fresh)
Source (fresh)
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TRAPP Replication
Bounded Cache
4, 7
2, 4
6, 10
Refresh when value exceeds bounds
5 8
3 4
Source (fresh)
Source (fresh)
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TRAPP Replication
you decide
Bounded Cache
performance
AVG ? 4, 7
6, 10
2, 4
precision
8
4
Source (fresh)
Source (fresh)
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Outline

• TRAPP Architecture
• Query Execution for Bounded Answers
• Adjusting Bound Width
• Related Work
• Status and Future Work

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Overview of TRAPP

• Caches store bounds that include exact source
  values
• Sources refresh when value exceeds bound
• Queries over cached data include a precision
  constraint
• Our algorithms answer queries by refreshing as
  few values as possible to meet precision
  constraint

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Example TRAPP Query
Bounded Cache
AVG ? 4, 7 want within 1
6, 10
2, 4
8
4
Source (fresh)
Source (fresh)
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TRAPP Architecture
query precision constraint
bounded answer
Source
value-initiated refresh
Cache
Refresh Monitor
query-initiated refresh
Query Processor
query-initiated refresh request
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Precision-Performance Tradeoff
stale cache
TRAPP
performance
exact cache
precision

• Higher precision requires more refreshing
• Higher performance forces low precision

TRAPP offers a continuous tradeoff
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Application Network Monitoring
latency bandwidth traffic
latency bandwidth traffic
latency bandwidth traffic
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Query Execution for Bounded Answers

• Input
• Query aggregation w/selection predicate
• Precision constraint
• Set of bounded values with cost to refresh each
• Step 1 Compute initial bounded answer
• Step 2 Determine minimum-cost set of values to
  refresh that guarantee satisfaction of the
  precision constraint
• Step 3 Use exact values from refreshes combined
  with bounds to compute final bounded answer

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Example Query SUM

• SELECT SUM(A) WITHIN 2
• Steps 1 3 (computing bounded answer)

?
A
Li , Hi ? Li , ? Hi
L1, H1 L2, H2
2, 3 4, 8 6, 11
example
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SUM, Choosing Tuples to Refresh

• Isomorphic to 0/1 Knapsack Problem
• Objective fill knapsack with bounds that would
  be expensive to refresh while not exceeding
  capacity
• Knapsack contents set of bounds not to refresh
• Benefit cost saved by not refreshing
• Knapsack capacity precision constraint
• Weight bound width
• Knapsack is NP-Hard -- we use ?-approximation
  algorithm by Ibarra, Kim

• Observation width of answer bound sum of
  non-refreshed bound widths
• We need this quantity to be less than the
  precision constraint

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SUM with a Selection Predicate

• SELECT SUM(A) WITHIN 2 WHERE B gt 10
• Three possibilities for each B value
• LBi gt 10 (e.g., 15, 20) yes
• HBi ? 10 (e.g., 5, 8) no
• else (e.g., 9, 12) maybe
• Ignore nos and process yess as before
• For maybes, pretend that bound on A includes 0
• e.g., A ? 3, 5 becomes A ? 0, 5

A
B
LA1, HA1 LA2, HA2
LB1, HB1 LB2, HB2
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Other Aggregation Functions

• COUNT
• MIN/MAX
• AVG
• MEDIAN
• see STOC00

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Realizing the Precision-Performance Tradeoff
0
1000
2000
3000
4000
150 100 50
0
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Adjusting Bound Width

• Dynamically adjust bound width to minimize the
  probability of a refresh
• Preliminary results indicate that this adaptive
  algorithm is promising

value-initiated refresh or
query-initiated refresh
value exceeds bounds (bound was too narrow)
more precision required (bound was too wide)
grow
shrink
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Not Covered in Talk See Paper

• Details on other aggregates
• Many more examples
• Joins
• Time-varying bounds L(t), H(t)

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Related Work

• Approximate answers
• Mostly precomputation or sampling to provide
  statistical results
• Reduce representation size
• e.g., Multi-resolution data model Read et al.
• Still fetch all objects

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Related Work (cont.)

• Bounds on numerical values
• e.g., Quasi-copies Alonso et al., Moving
  Objects Databases Wolfson et al., Demarcation
  Protocol Barbara/Garcia-Molina
• No user control of precision-performance tradeoff
• e.g., APPROXIMATE Jukic/Vrbsky, Constraint
  Databases, Incomplete Information Databases
  Abiteboul et al.
• Bounded values are not approximations of exact
  values available at cost
• Bounds on the number of updates
• e.g., Divergence Caching Huang et al.
• No bounds on the values themselves

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Status and Future Work

• Underway
• Performance study on bound functions and width
  adjustment algorithms
• Non-numeric data (e.g., WWW)
• Multi-level replication systems
• Other types of queries
• Iterative refresh algorithms
• Delaying the propagation of insertions and
  deletions
• Planned
• Investigation of real-time and consistency issues
• Applying TRAPP to data visualization

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Thats all folks!

• To contact me
• olston_at_db.stanford.edu
• http//www.db.stanford.edu/olston