Localized Algorithms In Wireless Ad Hoc Networks

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Localized Algorithms In Wireless Ad Hoc Networks
Seapahn Megerian megerian_at_ece.wisc.edu Electrica
l and Computer Engineering Department University
of Wisconsin Madison
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Wireless Ad-Hoc Sensor Networks
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Wireless Ad-Hoc Sensor Networks
GATEWAY
MAIN SERVER
CONTROL CENTER
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Wireless Ad-Hoc Sensor Networks
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Wireless Ad-Hoc Sensor Networks
Localized Distributed
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Sensor Network Applications

• Monitoring seismic activity in earthquake prone
  regions
• Observing ground movements
• Buildings and high rises
• Environmental monitoring in buildings
• temperature, lighting, etc.
• Smart classrooms
• Military
• Even other planets sensors on Mars

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Quality of Service

• Multimedia and the Internet
• QoS widely studied
• Can have different meanings
• Resolution and frame rate in video streams
• Latency, bandwidth in wired links
• Sensor networks
• Ability to detect events
• Latency of detection (and reporting)
• Accuracy
• Will depend strongly on errors and noise

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Objectives Localized Algorithm

• Generic technique for solving distributed
  optimization problems in wireless networks
• Take into account topology, available energy,
  power, privacy requirements, etc.
• Obtain only needed information and use it to
  guide optimization
• Take into account problem properties
• Problems Numerical errors

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Talk Organization

• Localized Algorithms A definition?
• Localized vs. centralized
• Localized vs. classic distributed computation
• Related work
• Location discovery and sensor exposure
• Exposure preliminaries and background
• Localized minimal exposure path algorithm
• Open problems and research directions
• Conclusion

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Localized Algorithms

• Localized algorithms for wireless networks
• Take into account geographical properties
• Relative communication and computation costs much
  higher and often difficult to predict
• Unreasonable and often unnecessary to expect
  results with very high accuracy
• Energy consumption
• Privacy and security issues

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Localized vs. Centralized

• Centralized equal or better if data available
• Centralized much better understood
• Complexity theory and NP-completeness
• Hard centralized problem -gt hard localized
• Heuristics for hard problems
• Question How about easy problems?
• Example Which polynomial-time algorithms can be
  implemented easily under localized computation
  models?

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Localized vs. Distributed

• Distributed computing paradigms
• Classical distributed Fault tolerance
• Parallel computing Speed is everything
• Internet Scaling, Security
• Correctness of results is a major assumption
• Regular structures and architectures
• Known or predictable cost models (e.g. latency)

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Parallel Algorithms

• Sorting
• Searching
• Matrix operations
• Multiply, inverse, linear solve
• Dense vs. Sparse
• Trees and graphs
• Shortest paths

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Distributed algorithms - Networking

• Some algorithms are very well studied
• Routing (path finding)
• Resource assignment
• MAC
• Addressing, clustering, multiplexing
• Storage and caching

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Localized Algorithm Paradigms

• 1. Guarantee solution quality while minimizing
  computation cost
• Q Localized Q Centralized
• Minimize Messages exchanged
• Minimize Energy consumption
• Minimize Latency
• 2. Optimize solution quality with guarantee on
  computation costs
• Minimize (Q Centralized - Q Localized)
• Minimize Number of nodes contacted
• Minimize Messages exchanged
• Minimize Latency

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Related Work

• Distributed Algorithms
• Nancy Lynch. Distributed Algorithms. Morgan
  Kaufman Publishers, San Mateo, CA, 1996.
• C.A.R. Hoare. Communicating Sequential Processes.
  Prentice-Hall International, 1985.
• E.H. Durfee, V.R. Lesser, D.D. Corkill, Trends in
  Cooperative Distributed Problem Solving. IEEE
  Transactions on Knowledge and Data Engineering,
  Vol.1, pp. 63-83, March 1989.

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Related Work Localized Algorithms

• Distributed Optimization in Sensor Networks
  IPSN04Michael Rabbat, Robert Nowak (UW Madison)
• Incremental subgradient methods for optimization
• Distributed classification and estimation
• Locally Constructed Algorithms for Distributed
  Computations in Ad-Hoc NetworksIPSN04 Dzulkifli
  Scherber,Babis Papadopoulos (University of
  Mayland)
• Distributed linear dynamic systems built locally
• Signal estimation from multi-node noisy
  observations

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Related Work

• Location Discovery
• A. Savvides, C. Han, M. Srivastava. Dynamic
  Fine-Grained Localization in Ad-Hoc Networks of
  Sensors. MobiCOM01.
• N. Priyantha, A. Miu, H. Balakrishnan, S. Teller.
  The Cricket Compass for Context-Aware
  Applications. MobiCOM01.
• Sensor Coverage
• S. Meguerdichian, F. Koushanfar, G. Qu, M.
  Potkonjak. Exposure In Wireless Ad-Hoc Sensor
  Networks. MobiCOM01.
• S. Meguerdichian, F. Koushanfar, M. Potkonjak, M.
  Srivastava. Coverage Problems in Wireless
  Add-Hoc Sensor Networks. IEEE Infocom01

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Localized Algorithm Components

• Data acquisition mechanisms
• Optimization mechanisms
• Search expansion rules
• Bounding conditions
• Termination rules

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Location Discovery

• Beacon Nodes
• GPS equipped
• Predeployed at known locations
• Distance estimation step
• Atomic Step Multilateration
• Optimization step
• Major Challenge
• Dealing with measurement errors
• GPS
• Distance estimates

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Localized Location Discovery

• Optimization Step
• Within one hop neighborhood select best candidate
  for final location assignment
• Repeat information exchange and optimization
  until all nodes have assigned locations
• Orphan nodes may exists
• Nodes with less than 3 neighbors who can
  determine their location.

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Sensor Coverage

• Given
• Field A
• N sensors
• How well can the field be observed ?
• Closest Sensor (minimum distance) only
• Worst Case Coverage Maximal Breach Path
• Best Case Coverage Maximal Support Path
• Multiple Sensors speed and path considered
• Minimal Exposure Path

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Exposure An Introduction
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Sensor Exposure
Suppose S(s ,p) represents the non-negative
sensibility of sensor s to the point p. For
example
The Exposure for an object in the sensor field
during the interval t1,t2 along the path p(t)
is
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Exposure Coverage Problem Formulation

• Given
• Field A
• N sensors
• Initial and final points I and F
• Problem
• Find the Minimal Exposure Path PminE in A,
  starting in I and ending in F.
• PminE is the path in A, along which the exposure
  is the smallest among all paths from I to F.

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Minimal Exposure Path Algorithm

• Use a grid to approximate path exposures.
• The exposure (weight) along each edge of the grid
  approximated using numerical techniques.
• Use Dijkstras Single-Source Shortest Path
  Algorithm on the weighted graph (grid) to find
  the Minimal Exposure Path.

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Localized Exposure Field Partitioning

• Voronoi Partitioning
• Advantages
• One sensor per Polygon
• Node can calculate its VP by knowing only its
  immediate (Delaunay) neighbors
• Smaller VPs in high node density areas
• Drawbacks
• One sensor potentially in charge of large area
• Paths likely to be close to border edges
• How to find Delaunay neighbors?

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Localized Exposure Continued

• Each polygon edge has a corresponding Exposure
  Profile (EP)
• Can use different data structures to store EPs.
• EPs initialized to infinity
• Continuously updated in algorithm by keeping
  smaller values and discarding larger ones

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Localized Exposure Continued

• Node s1 updates an EP e13
• s1 sends update message to neighbor node s3
• s3 computes new minimal exposure paths and
  updates all its EPs.
• s3 sends appropriate EP update messages to
  corresponding neighbors

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Localized Exposure Continued

• Algorithm stops when
• Each EP at the search boundary is larger than the
  specified termination condition (parameter
  indicating bound on exposure)
• Specified by the algorithm at first
• Periodically set to exposure at destination point
  during the optimization process (broadcast)
• No more edge updates (EP)
• Guaranteed to converge since exposure is always
  increasing.

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Localized Exposure Message Types

• Path_request Node si receives a request from an
  agent to find PminE from I to D .
• Edge_update Node si receives an update
  notification from a neighbor to continue search
  for PminE(I,D).
• Abort_update Aborting conditions notification.
• Dest_update Destination reached notification

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Localized Exposure Caveat

• At times, minimal exposure paths may lie close to
  polygon edges
• Numerical errors and data structure limitations
  can cause cycles to develop between neighboring
  nodes
• Each believes the other has better path to
  destination
• Possible Solution
• Accept improvement at each point in an EP update
  message based on a threshold
• Discard small improvements
• Prevents infinite loops and unnecessary update
  messages
• Solution will be slightly inaccurate

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Abort Conditions Optimization

• Abort Updates
• Parameter indicating the search frontier
• Increase when unsuccessful
• Destination Reached Updates
• No need to expand paths that have exposure larger
  than current path to destination

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Localized Minimal Exposure Path
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Localized Algorithms Summary

• Ad-Hoc wireless (sensor) networks
• Classical distributed algorithms not suitable
• Localized algorithms
• Leverage on specific wireless network properties
• Take into account inherent costs
• Energy Consumption
• Large communication overheads
• Inaccurate measurements
• Two examples
• Location Discovery
• Minimal Exposure Paths
• Many interesting open problems

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The End
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Localized Minimal Exposure Path