Algorithmic Models for Sensor Networks

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Algorithmic Models for Sensor Networks

• Schmid, Wattenhofer
• IPDPS06

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Models and Sensor Networks

• To develop algorithms and mathematically prove
  their correctness, simplifying models are needed
  for WSNs.
• Balance between simplifying the model in order to
  keep the analysis tractable and neglecting
  important properties of the nw
• Common representations are as a graph, geometric
  representation.

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Connectivity Models

• Given a set of nodes, which nodes can recv the
  transmission of a given node
• Is u adjacent to v ?
• Typically symmetric.
• Classic model UDG
• Transmission range normalized to 1

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UDG

• Idealistic since real radios are not omni
  directional and even small obstacles affect
  connectivity
• Proposed General Graph

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Connectivity models (contd.)

• Too pessimistic!
• Something between
• the 2 extremes.
• QDG with ?1 is a
• UDG

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UDG to QUDG

• Many algorithms can be transformed from UDG to
  QUDG at a cost of 1/?2
• This ok for ?0.5 (4)
• But for ?0.1, much worse (100)
• Still does not translate nicely to obstacles like
  walls eg. All nodes on one side of the wall can
  talk to each other but not the opposite side

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Bounded Interference Graph (BIG)

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Extending the dimension

• 2d
• Nodes in 2d Euclidean
• plane form a doubling metric
• General graph does not

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Additional variations

• Antennas
• variations besides omni-directional
• Link failures model probabilistically

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Interference

• Important for lower layer protocols
• Most popular SINR Signal to Noise Interference
  Ratio
• Does not specify power. 3 ways

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Interference

• The SINR model is very complicated
• A lot of far away transmissions sum up as noise
  to a sender-receiver pair
• ONE is popular. UDG with one UDI shown next

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UDI UDG with Distance Inteference

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Hop based Interference

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Algorithms

• Global can operate on entire network
• Distributed a node has information about only
  its own state. Messages need to be exchanged to
  learn more about the nw. All nodes run their own
  algorithm
• Localized Special case of distributed. Limited
  to k. A node can retard its right to communicate
  i.e. some causality

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Other assumptions

• MAC ideal vs. interference (adversary)
• Random node distribution uniform distribution
  in 2d plane. Also Poisson
• Worst-case node distribution completely
  arbitrary
• Node ids again worst, random. Range can limit
  also

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Other assumptions

• Location info absolute or relative to other
  nodes.
• Sleep time energy consumption
• Lifetime definitions.

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Conclusion

• No one model
• Emphasized that for correctness, the more
  pessimistic or conservative models should be used
• Broad overview provided.