Medians and Beyond: New Aggregation Techniques for Sensor Networks

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Medians and Beyond New Aggregation Techniques
for Sensor Networks

• ACM SenSys04
• Nisheeth Shrivastava Chiranjeeb Buragohain
  Divyakan Agrawal Subhash Suri
• Presented by John Roh

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Contents

• Introduction
• Q-Digest (Quantile-Digest)
• Properties
• Building Q-Digest
• Merging Q-Digest
• Analysis of error bound
• Queries on Q-Digest
• Evaluations
• Summary

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Aggregation Query Processing(1/2)

• Aggregation Queries
• need aggregated answer, not a single raw reading
  
• E.g.) min, sum, avg and median

Quantile query What is the 50th sensor value,
when 100 sensors are deployed ? Reverse Quantile
query Consensus query What is the most frequent
value ?
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Aggregation Query Processing(2/2)

• Three well-known Techniques
• Direct delivery
• No in-network processing
• Packet merge
• No intermediate computation
• Partial aggregation
• in-network processing
• intermediate computation
• reduces comm. cost
• applied to sum, max, avg, min

applied to median in past
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Aggregation Query Processing in list
1. Base station initiate query 2. Query is
disseminated using routing tree 3. Sensor data
are collected into base station 4. Query is
answered
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The paper presents

• in-networking processing technique
• for approximated aggregation
• to answer
• Quantile query ( Nth ? value)
• Reverse Quantile query ( value ? Nth )
• Consensus query ( most frequent? )
• while providing strict error guarantees
• (input message size m)

There is a trade-off of error and message size m
!
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Aggregation Query Processing in Q-Digest
1. Base station initiate query 2. Query is
disseminated using routing tree 3. Q-Digests are
built collected into base station 3-1. Merge
childrens Q-Digest to construct new one 3-2.
Add nodes value to Q-Digest 3-3. Send Q-Digest
to parent node 4. Query is answered
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Q-Digest(Quantile-Digest)(1/2)

• data structure for compressed data
• used to in-networking processing
• for approximated aggregation

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Q-Digest(2/2)
Represented as
of sensor
Compression parameter
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Properties of Q-Digest
(1) Except leaf, no node should have a high count
(2) Except root, we achieve an effect of
compression
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Building Q-Digest(1/2)
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Building Q-Digest(2/2)
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Merging Q-Digest(1/2)
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Merging Q-Digest(2/2)
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Analysis of error bound
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Queries on Q-Digest(1/2)
Q-Digest is represented as

• Quantile Query
• input
• q 01
• output
• value of qnth?
• 0.5 q
• median
• Reverse Query
• input
• value
• output
• kth?

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Queries on Q-Digest(2/2)
Q-Digest is represented as

• Consensus Query
• The most frequent value?
• output
• value

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Evaluation

• Settings
• Routing tree
• Breadth first search tree
• Sensor field
• 1000 x 1000 area with 1000 sensor nodes
• 2000 x 2000 area with 4000 sensor nodes
• 2800 x 2800 area with 8000 sensor nodes
• Sensor value
• Random
• Correlated United States Geological Survey

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Error and Message Size
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Total Data Transmission
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Residual Power
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Conclusion

• Energy-efficient in-networking processing
  technique
• for approximated aggregation
• to answer more complex query such as
• Quantile query
• Reverse Quantile query
• Consensus query
• with strict error guarantees
• (input message size m)