PeertoPeer Spatial Queries in Sensor Networks

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Peer-to-Peer Spatial Queries in Sensor Networks

• Murat Demirbas
• Hakan Ferhatosmanoglu
• The Ohio State University

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Sensor networks

• A sensor node
• 8K RAM, 4Mhz processor
• magnetism, heat, sound, vibration, infrared
• wireless communication up to 200 feet
• costs 10 (right now costs 100)
• Applications include
• ecology monitoring, precision agriculture
• military and surveillance
• In OSU, we developed a tracking service for
  DARPA-NEST
• classify trespassers as car, soldier, civilian
• report the tracking information to a base-station
  (laptop) for visualization

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Spatial queries in sensor networks

• The primary goal of sensor networks is to monitor
  spatial information about a region of interest
• Nearest neighbor (NN) queries are essential
• What is the location of the nearest data object
  to (x,y) ?
• Database systems
• R-tree for efficient execution of nearest
  neighbor queries

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Challenges in sensor networks

• energy constrained nodes, network contention
• programs should avoid excessive communication
• centralized programs are not suitable
• work in database systems not readily applicable
• faults
• data is noisy
• nodes fail in complex ways
• on site maintenance is not feasible
• self-healing programs are needed

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P2P spatial queries in sensor networks

• Pursuer- evader tracking
• A pursuer should be able to query a node for the
  location of the closest evader
• Every node is a peer
• each node (not only the base-station) can insert
  a query
• each node can participate in the processing of
  the query
• query is processed as local as possible

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Our contributions

• We present a peer-to-peer query processing system
  where
• only the relevant nodes for the correct execution
  of the query are involved in the query execution
  (for minimizing energy and response time)
• the indexing structure, peer-tree, is
  self-stabilizing (for achieving eventually
  correct answers in the presence of faults)

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Outline

• Model
• Peer-tree structure
• P2P nearest neighbor queries
• Pursuer evader tracking revisited
• Conclusions

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Model

• Geometric network model (2-D)
• Connected graph duplex links
• Transient faults
• Maximal parallelism in node actions

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Outline

• Model
• Peer-tree structure
• P2P nearest neighbor queries
• Pursuer evader tracking revisited
• Conclusions

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R-tree structure

• Approximately balanced tree
• A node holds n to 2?n (c,mbr) pairs
• c is the child pointer
• mbr is the minimum bounding rectangle (MBR) of
  all rectangles at c
• Rectangles at any level may be overlapping
• Every descending path in the tree is a sequence
  of nested rectangles with the last one containing
  the actual data

A
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Peer-tree construction

• Hierarchical partitioning of a sensor network
  based on the number of nodes (n to 2?n) contained
  at each cluster
• every node cooperates at level 1 of the
  partitioning
• only clusterheads of level i cooperate for level
  i1
• Every node v maintains
• l.v highest level of construction v has
  cooperated
• p.v(i), 0ltiltl.v parent of v at level i
• c.v(i), 0ltiltl.v children of v at level i
• mbr.v(i) MBR of v(i) calculated using c.v(i)
• Peer-tree is the tree that c pointers embed over
  the network
• Two actions
• Join/form cluster
• Split a cluster

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Join/form a cluster

• v executes a join/form cluster action if l.vi
  yet p.v(i)nil
• v searches for a node with l i1, at
  increasingly larger radii
• if such a node is encountered v joins that nodes
  cluster
• Else, if v encounters n nodes with li during its
  search
• v waits for a random time (to avoid formation of
  multiple clusters that are concurrently started
  by multiple nearby nodes)
• if v is not contacted within this wait, v forms a
  cluster
• p.v(i)v, l.vi1,
• c.v(i1) is set, mbr.v(i1) is calculated

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Split cluster

• During concurrent executions of join/form cluster
  action by multiple nodes, a level i clusterhead v
  may end up with gt 2?n children
• v assigns extra level i clusterheads among its
  children and ensures that each cluster has n to
  2?n nodes

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Peer-tree
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Self-stabilization of peer-tree

• vs ith level cluster is collapsed if
• c.v(i)ltn, or
• there is a node u in c.v(i) s.t.,
• u ? mbr.v(i), or
• p.u ? v
• the nodes in the collapsed cluster join
  neighboring clusterheads or form their clusters

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Outline

• Model
• Peer-tree structure
• P2P nearest neighbor queries
• Pursuer evader tracking revisited
• Conclusions

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NN queries over traditional R-tree

• The search starts from the root (highest) level,
  and performs a traversal of the relevant MBRs
• The MBRs that are guaranteed not to have the
  closest data point are pruned
• e.g., MINDIST, the shortest possible distance
  from a point in an MBR to (x,y), is larger than
  the current candidate for NN
• At every iteration, the algorithm
• sorts the MBRs with respect to their MINDIST,
• considers the first item in the list, expands its
  children, and inserts them to the list for
  processing

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P2P NN queries over Peer-tree

• Any node in the network can submit an NN query
  concerning any coordinate (x,y)
• If the query can be answered locally, there is no
  need to propagate it till the root (highest)
  level
• query is propagated up if (x,y) is not enclosed
  within current MBR
• At some level a clusterhead that contains (x,y)
  is reached
• from this point on, the query is sent to children
  
• children are ordered with respect to MINDIST
• this way only the most relevant children are
  queried

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NN query execution
(x,y)
query
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NN query execution
(x,y)
query
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P2P NN queries

• If (x,y) is not within MBR of v at level i,
  mbr.v(i), then forward query to p.v(i)
• let u be the first encountered clusterhead that
  contains (x,y)
• u forwards query to relevant children in c.u
• While the query is traveling downwards, each
  clusterhead
• sorts the children wrt MINDIST
• prunes list using the replies from queried
  children
• A level 0 node returns its nearest distance NN,
  reply is propagated up
• u aggregates the replies
• if (x,y) is encapsulated by c.u, the reply is
  sent to querying node
• else, u punts the query to its clusterhead

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NN query execution
(x,y)
query
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Tradeoff time vs. energy

• Minimal response time
• The clusterhead forwards the query to its
  relevant children in parallel (concurrent
  execution)
• Minimal energy consumption
• The clusterhead forwards the query to its
  relevant children sequentially (to maximize
  pruning)
• Optimizing both
• Hybrid of the above

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Outline

• Model
• Peer-tree structure
• P2P nearest neighbor queries
• Pursuer evader tracking revisited
• Conclusions

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Pursuer-evader problem

• Evader is omniscient Strategy of
  evader is unknown
• Pursuer can only see state of nearest
  node Pursuer moves faster than evader
• Required is to design a program for nodes and
  pursuer so that pursuer can catch evader (despite
  the occurrence of faults)
• Demirbas, Arora, Gouda

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Evader-centric program (cont.)

• Tracking tree is dynamically rooted at the evader
• Parent of a node is closer to the evader

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Evader-centric program (cont.)

• Tracking tree is dynamically rooted at the evader
• Parent of a node is closer to the evader

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Evader-centric program (cont.)

• Tracking tree is dynamically rooted at the evader
• Parent of a node is closer to the evader

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Pursuer-evader tracking viaP2P spatial queries

• The pursuer submits an NN query with its own
  location to find out the location of the nearest
  evader to itself
• On demand approach
• No tracking tree is maintained, a clusterhead is
  only aware of the existence of an evader in its
  region, but does not know where it is

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Conclusions

• We have presented for the first time a
  peer-to-peer spatial query processing system for
  sensor networks
• We are implementing this system in the context of
  our work on tracking services for sensor network
  (LITS)
• Indexing in database systems, peer-to-peer
  systems, sensor networks have a lot of
  similarities (as well as distinctions)
• peer-tree is based on R-tree concept in database
  systems
• possible to extend peer-tree for wired systems
• since energy is no longer an issue, scalability
  and load balancing can be improved by inserting
  long links