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Tributaries and Deltas: Efficient and Robust Aggregation in Sensor Network Streams

Tributaries and Deltas: Efficient and Robust Aggregation in Sensor Network Streams

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Tributaries and Deltas: Efficient and Robust Aggregation in Sensor Network Streams

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  1. Tributaries and Deltas: Efficient and Robust Aggregation in Sensor Network Streams Amit Manjhi, Suman Nath, Phillip B. Gibbons Carnegie Mellon University Intel Research Pittsburgh

  2. Background: Sensors Constraints: • Conserving battery power is important • Communication consumes orders of magnitude more energy than local computation • Operate in dynamic, harsh environments Battery-powered tiny devices • Used in Eco-system monitoring at James Reserve, Habitat monitoring at Great Duck Island, etc. Amit Manjhi, SIGMOD '05

  3. Background: Sensor networks Important type of query is computing aggregates e.g., total number of live sensors In-network aggregation is performed to save communication Count 3 3 Amit Manjhi, SIGMOD '05

  4. - Non-robust topology Existing energy-efficient in-network approaches: Tree and Multi-path Tree [TinyDB, Cougar] Multi-path [Considine et al. ICDE ‘04] + Robust Topology + Exact answer - Approximate answer Amit Manjhi, SIGMOD '05

  5. Tree and Multi-path Tradeoffs Robust topology Exact answer Loss rate varies with change in conditions Can we get the best of both by adapting to changing loss rates? Amit Manjhi, SIGMOD '05

  6. Our solution: Tributary-Delta Delta (Multi-path region) • Simultaneously run Tree and Multi-path in different parts of the network • As energy-efficient as tree or multi-path • Multi-path region adapts to loss rate Tributary (Tree region) Amit Manjhi, SIGMOD '05

  7. Outline • Background and motivation • Tributary-Delta • Simple aggregates in TD framework • Frequent Items in TD framework • Evaluation • Related work and conclusion Amit Manjhi, SIGMOD '05

  8. How does Tributary-Delta work? • Correctness: A tree node should not receive aggregates from a multi-path node • Gives rise to a delta at the centre (multi-path aggregation is used in the nodes at the centre) Delta (Multi-path region) Delta T T Tributary (Tree region) T T Amit Manjhi, SIGMOD '05

  9. How does Tributary-Delta adapt? • Expand or shrink the delta region • Expand delta  increases robustness • Shrink delta  lowers approximation error Delta TD-Coarse: uniform expansion TD: focused expansion Tributary Amit Manjhi, SIGMOD '05

  10. Computing Aggregates in the Tributary-Delta Framework 3. Nodes at the boundary Conversion Function: Convert tree results to multi-path results 2. Each multi-path node Multi-path Algorithm: Generate multi-path partial results 1. Each tree node Tree Algorithm: Generate tree partial results Amit Manjhi, SIGMOD '05

  11. Example Aggregates • Many useful aggregates can be readily computed within the Tributary-Delta framework • Missing piece: a suitable conversion function • We provide conversion functions for several aggregates • Count • Sum, Average • Top-k • Uniform sample Amit Manjhi, SIGMOD '05

  12. 2 1 3 0 1 1 2 3 2 2 Computation of “Count” • Tree Algorithm is simple • Multi-path Algorithm • [AMS STOC’96] 3 3. Conversion function: receive count 3, repeat “coin toss” 3 times, and take maximum 3 3 • T T T H: report 3 • Probability of obtaining ‘i’ proportional to 2-i • To combine multi-path partial values, take the maximum • Max. value is i, estimate is 2i 1 3 1 1 Amit Manjhi, SIGMOD '05

  13. Outline • Background and motivation • Tributary-Delta • Simple aggregates in TD framework • Frequent Items in TD framework • Evaluation • Related work and conclusion Amit Manjhi, SIGMOD '05

  14. Finding Frequent Items • Tree Algorithm: • Previous work [Greenwald, Khanna PODS ’04, Manjhi et al. ICDE ‘05] • Our tree algorithm achieves optimal bound for total communication • Multi-path Algorithm: • Previous work [Nath et al. SenSys ’04] • Our multi-path algorithm is more accurate than previous work • Conversion Function Amit Manjhi, SIGMOD '05

  15. Formal Problem Statement Approximate Answers 1% 0.9% … Find items that are more frequent than 1% with error 0.1% Formulate problem as [Manku, Motwani VLDB’02, Manjhi et al. ICDE ’05] Frequency Counts Amit Manjhi, SIGMOD '05

  16. Framework for finding Freq. Items 1. Add frequency counts from children 2. Decrement frequency counts 3. Drop counters that are below zero These steps are repeated at each internal node; decrements depend on height in the tree Amit Manjhi, SIGMOD '05

  17. How much to decrement at different levels? Early Drop Max possible error  Minimizes total communication Error Minimizes communication on any link Geometric decrease in decrement, e.g.: 0.5%, 0.25%, 0.125%,… 0.5%, 0.75%, 0.875%,…., =0.1% • Need to balance two competing pressures: • Early reduction of data (near leaf) • Informed reduction of data (near root) Late Drop Exact Height Leaf Root Amit Manjhi, SIGMOD '05

  18. Multi-path Algorithm for Freq. Items 1. Add  Duplicate insensitive addition Yes 2. Decrement  Duplicate insensitive subtraction No 3. Drop counters below zero Yes 2. Drop counters below (rising) threshold Yes Threshold is maintained based on careful analysis Paper has details on lowering communication Amit Manjhi, SIGMOD '05

  19. Outline • Background and motivation • Tributary-Delta • Simple aggregates in TD framework • Frequent Items in TD framework • Evaluation • Related works and conclusion Amit Manjhi, SIGMOD '05

  20. Evaluation Methodology • The TAG Simulator [Madden et al. OSDI ‘02] • Topology: 600 random sensors in 20 x 20 • Base station is at the center • Approaches: • Tree-based scheme: TAG • Multi-path scheme: Synopsis Diffusion [Nath et al. SenSys ‘04] • TD-Coarse: uniform expansion • TD: focused expansion Amit Manjhi, SIGMOD '05

  21. Effects of regional loss rate Loss rate = 0.05 Varying loss rate All four approaches use same energy Amit Manjhi, SIGMOD '05

  22. Effects of global loss rate Varying loss rate 1. Our methods effectively combine the benefits: perform better than either existing approach 2. All four approaches use same energy Amit Manjhi, SIGMOD '05

  23. Computation of frequent items False positives < 3% Data from real sensor deployment Loss rate = 0.05 Varying loss rate Amit Manjhi, SIGMOD '05

  24. Other results in paper • Adaptation details • Tree construction algorithm that reduces communication • 2-approximation for total and maximum load, and extension to quantiles • More extensive evaluation Amit Manjhi, SIGMOD '05

  25. Related Work • Existing in-network aggregation algorithms • Tree: TinyDB [Madden et al. SIGMOD ’03] • Multi-path: Considine et al. ICDE ’04, Bawa et al. SIGMOD ’04, Nath et al. SenSys ‘04 • Adapting to changes in the environment • Directed Diffusion [Intanagowiwat et al. MobiCOM ’00], TAG [Madden et al. OSDI ’02] • Frequent items and quantiles • Manku, Motwani VLDB ’02, Greenwald, Khanna PODS ’04, Manjhi et al. ICDE ‘05 Amit Manjhi, SIGMOD '05

  26. Conclusion • Tributary-Delta: energy-efficient, and robust solution • Combines benefits of existing tree- and multi-path based approaches • Adapt to changing network conditions • Algorithms for finding frequent items • Results confirm the advantages • Error reduction is up to a factor of 3 Amit Manjhi, SIGMOD '05

  27. Future Work • Deployment in a real scenario —incorporate in TinyDB • Add other aggregates to the suite of aggregates Amit Manjhi, SIGMOD '05

  28. Back-up slides! Amit Manjhi, SIGMOD '05

  29. Adaptation Details Ask application for a threshold on percentage contributing Base station gets overall numbers on % contributing < > Increase delta region Decrease delta region Amit Manjhi, SIGMOD '05

  30. Tree Construction Algorithm – (1/2) Tree links are subset of ring links Ring 2 Avoid expensive synchronization Amit Manjhi, SIGMOD '05

  31. Tree Construction Algorithm – (2/2) Opportunistic parent switching: Each node of height i+1 should have at least 2 nodes of height i Each i+1 height node pins any two of its height i nodes, and then flags itself. Ring 2 2 3 1 2 2 3 1 Any non-pinned node can switch parent to a non-flagged node 2 1 1 1 1 Amit Manjhi, SIGMOD '05

  32. Multi-path over Rings • Each node transmits once = optimal energy cost (same as Tree) • A node is in ring i if it is i hop away from the base-station • Broadcasts by nodes in ring i are received by nodes in ring i-1 Ring 2 Amit Manjhi, SIGMOD '05

  33. A 2-approximation Solution Early Drop Max possible error  Minimizes total communication Error Minimizes communication on any link 2-approx on both objectives Late Drop Exact Height Leaf Root Amit Manjhi, SIGMOD '05

  34. Minimizing total communication for quantiles • Original algorithm by Greenwald, Khanna PODS ’04 • Vary the size of quantiles in a geometric pattern, and the total communication is linear in the number of sensor nodes. Amit Manjhi, SIGMOD '05

  35. Extensive Evaluation • Evaluation of our frequent items tree algorithm • Evaluation of our frequent items multi-path algorithm • How quickly TD and TD-Coarse respond to changes in loss rates? Amit Manjhi, SIGMOD '05