Medians and beyond new aggregation techniques for sensor networks
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Medians and Beyond: New Aggregation Techniques for Sensor Networks. CS851 Seminar Presentation. Outline. Motivations, State of Art, Contributions The Q-Digest Scheme Queries on Q-Digest Experimental Evaluation Conclusions Be prepared! I have questions for you!. Motivations.

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Medians and beyond new aggregation techniques for sensor networks

Medians and Beyond: New Aggregation Techniques for Sensor Networks

CS851 Seminar Presentation


Outline

Outline

  • Motivations, State of Art, Contributions

  • The Q-Digest Scheme

  • Queries on Q-Digest

  • Experimental Evaluation

  • Conclusions

    Be prepared! I have questions for you!


Motivations

Motivations

  • Trade Computation for Communication

    • Transmitting one bit over radio is at least three orders of magnitude more expensive in terms of energy consumption than executing a single instruction

  • Support Aggregation Queries

    • Need aggregated answer, not a single raw reading

    • Quantile query

      • Nthvalue

    • Reverse quantile query

      • Value  Nth

    • Consensus query

      • Most frequent?

    • Histogram


State of art

State of Art

  • TinyDB project in Berkeley & Cougar project in Cornell

    • Pros:

      • Energy efficient in-network data aggregation

      • Work very well in singleton sensor values

        • MIN, MAX, AVERAGE, SUM, COUNT

    • Cons:

      • Do not deal with complex aggregate measures

        • Median, Quantile, Reverse Quantile, Consensus

  • [Zhao et. al. 2003]

    • Algorithms for constructing summaries like MAX, AVG

    • Focus more on network monitoring and maintenance

  • [Przydatek et. al. 2003]

    • Secure aggregation


Contributions

Contributions

  • Propose Q-Digest for Approximated Aggregation

  • Provide Strict Theoretical Guarantees on the Approximation Quality of the Queries in Terms of the Message Size

  • Evaluate the performance of Q-Digest in Simulation


Roadmap

Roadmap

  • Motivations, State of Art, Contributions

  • The Q-Digest Scheme

  • Queries on Q-Digest

  • Experimental Evaluation

  • Conclusions and Discussions


Properties of q digest

Properties of Q-Digest

  • Each node v in tree T is a bucket;

    • Whose range [v.min, v.max] defines the position and width of the bucket;

    • Has counter count(v);

  • Given the compression parameter K, a node v is in q-digest iff it satisfies:

    • (1) If not a leaf, no high count;

    • (2) If not the root, a node and its children should not have low count;

  • A q-digest is a set of buckets of different sizes and their associated counts;


Building a q digest

Building a Q-Digest

  • Going bottom up to check whether any node violates digest property (2)

    • If yes, delete itself and its sibling, and merge to its parent;

  • Key feature of q-digest: Detailed information concerning data values which occur frequently are preserved in the digest, while less frequently occurring values are lumped into larger buckets resulting in information loss.


Merging q digest

Merging Q-Digest

  • Parent node merge Q1(n1,K) and Q2(n2,K) from children

How about merging Q1(n1,k1) and Q2(n2,K2)?

  • Each node has different communication ability

  • Each node has different power level

  • Powerful node can have bigger K while less powerful node can have smaller K value. Can we still get the same accuracy? Is that feasible?


Space complexity and error bound 1 4

What dos it mean 3K?

3K bites?

Space Complexity and Error Bound (1/4)

The root node does not satisfy property (2).??

3K means 3K

<nodeID(v), count(v)>

pairs


Space complexity and error bound 2 4

Space Complexity and Error Bound (2/4)

What about the leaf node, which does not satisfy property (1)?

It doesn’t matter, because a leaf node is not the ancestor of any node.


Space complexity and error bound 3 4

Space Complexity and Error Bound (3/4)


Space complexity and error bound 4 4

Space Complexity and Error Bound (4/4)


Representation of a q digest

Representation of a Q-Digest

  • Now to transmit the q-digest we send a set of tuple of the following form <nideID(v), count(v)> which requires a total of bits for each tuple.


Roadmap1

Roadmap

  • Motivations, State of Art, Contributions

  • The Q-Digest Scheme

  • Queries on Q-Digest

  • Experimental Evaluation

  • Conclusions and Discussions


Quantile query 1 3

Quantile Query(1/3)

  • Quantile query:

    • Given a fraction 0<q<1, find the value whose rank in sorted sequence of the n values is qn.

  • Answer the query:

    • Sort nodes in q-digest in increasing v.max; breaking ties by putting smaller ranges first;

    • Scan the sorted list and add the counts of nodes;

    • For some node v, the sum becomes more than qn, and the v.max is reported as the estimate of the quantile;


Quantile query 2 3

Quantile Query(2/3)

  • The confidence factor

    • Why need this?

      • is the worst case error estimation, which only occurs for a very pathological input case

    • What is it?

      • Confidence factor is defined as:

        (maximum weight of any path from root to leaf in Q)/n


Confidence factor example

Confidence Factor Example

  • N=15, k=5, =8

1 1 5 7 3 3 3 3

(maximum weight of any path from root to leaf in Q)/n = 7/15

<

= 3 * log8 / 3K = 3*3/3*5 = 9/15


Roadmap2

Roadmap

  • Motivations, State of Art, Contributions

  • The Q-Digest Scheme

  • Queries on Q-Digest

  • Experimental Evaluation

  • Conclusions and Discussions


Performance evaluation

Performance 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

    • Sensor value

      • Random

      • Correlated :

        • United States Geological Survey

    • Compare with List scheme:

      • List: Report all (value, count)

        back to base station; no

        in-network aggregation;


Error and message size

Error and Message Size

  • 160 bytes message size can get 5% error

  • 400 bytes message size can get 2% error


Total data transmission

Total Data Transmission

  • Q-digest transmit less data than list

  • Random input needs more transmission than correlated data


Residual power

Residual Power

  • For every byte transmitted, one unit of 40000 unit of power is depleted.

  • (How about reception?)

  • In List, 0.02% nodes have residual power fraction less than ½.

  • (???)


Conclusions

Conclusions

  • Propose Q-Digest for Approximated Aggregation

  • Provide Strict Theoretical Guarantees on the Approximation Quality of the Queries in Terms of the Message Size

  • Evaluate the performance of Q-Digest in Simulation


Thank you

Thank you!


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