Multidimensional Range Queries in Sensor Networks

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Multi-dimensional Range Queries in Sensor Networks

• SenSys 03
• Xin Li, Young Jin Kim, Ramesh Govindan, Wei Hong

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Contents

• Overview
• Concepts and Technology
• Event insertion
• Range querying
• Analysis of DIMs
• Simulation
• Conclusion

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Overview of DIMs

• Events (multi-dimensional space) are mapped onto
  zones of the network (2-d space)
• Data Locality Events with comparable attribute
  values stored in same location in network
• Locality-preserving geographic hash
• Events are routed to and stored at that node
• Queries are routed to and resolved by appropriate
  nodes

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Zone

• Rectangle R on x-y plane (entire network)
• Subrectangle Z is a zone if Z is obtained by
  dividing R k times satisfying the following
  property
• After the i-th division, 1 i k, R is
  partitioned into 2i equal rectangles. If i is odd
  (even), the division is parallel to the y-axis
  (x-axis).
• k is the level of the zone, level(Z) k

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Zone Identification

• code(Z)
• Bit string of length level(Z)
• Starting from left of code string, if zone Z
  resides on the left half of R, bit equals 0, else
  1. For the next bit, if zone Z resides on the
  bottom half of R, bit is 0, else 1.
• addr(Z)
• Centroid of zone rectangle

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Zone Terminology

• Sibling subtree of a zone
• Left/right subtree rooted at the same parent zone
• Backup zone
• If the sibling subtree of a node is on the left
  (right), its backup zone is the rightmost
  (leftmost) zone in its sibling subtree

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Zones Example
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Associating Zones with Nodes

• Sensor field divided into zones, which can be of
  different sizes
• Zone ownership
• A owns ZA ? ZA is the largest zone that contains
  only node A
• Some zones may not have node owner ? backup(Z) is
  the owner

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Algorithm for Zone Ownership

• Each node maintains its four boundaries
• Initialize to network boundary
• Send messages to learn locations of neighbors
• If neighbor responds, node will adjust its
  boundaries accordingly
• Else boundary is undecided
• Undecided boundaries resolved during querying or
  event insertion

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Event Insertion

• Hashing an event to a zone
• Routing an event to its owner
• Resolving undecided zone boundaries during
  insertion

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Event InsertionHashing an Event to a Zone

• Have m attributes A1, A2, , Am and attribute
  values have been normalized
• To hash a k-bit zone code to an event
• For i in 1, m, if Ai lt 0.5, the ith bit of the
  zone code is 0, else 1.
• For i in m1, 2m, if Ai-m lt 0.25 or 0.5 Ai-m
  lt 0.75, then the (i-m)th bit is 0, else 1.
• Etc. until all k bits are assigned

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Event InsertionHashing an Event to a Zone

• Example Hash event lt0.3, 0.8gt to a 5-bit zone
  code
• First range 0 0, 0.5)
• Second range 0 0, 0.25), 0.5, 0.75)
• Third range 0 0, 0.125), 0.25, 0.375), 0.5,
  0.625), 0.75, 0.875)
• Zone code 01110

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Event InsertionRouting an Event to its Owner

• GPSR delivers message to node A
• Message contains event E, code(E), target
  location, owner, location of owner,
• A encodes the event to codenew(E)
• Updates message if codenew(E) is longer than code
  in message
• A checks if code(A) has longer match with code(E)
  than previous owner
• If yes, update message by setting itself as the
  owner
• If code(A) and code(E) identical and As
  boundaries are known, A is the owner of E and
  stores it
• Else A will route E to its owner by invoking GPSR

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Event InsertionResolving Undecided Boundaries

• Suppose node C receives event E
• If code(C) code(E) and all of Cs boundaries
  are known, C will store the event
• If C has undecided boundaries, there may be zone
  overlap with another node
• C sets itself as owner and forwards message using
  GPSR perimeter mode
• If message not changed, it will come back to C
• C assumes it is the owner and stores it

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Event InsertionResolving Undecided Boundaries

• An intermediate node X marks itself as the owner
  but code(E) is unchanged
• X recognizes zone overlap with C and adjusts its
  boundaries and messages C to update its
  boundaries
• An intermediate node D refines code(E)
• D will try to deliver the message to the new zone
• Another node X may overlap with C
• X will shrink its zone and send C messages to do
  the same
• C will update its undecided boundary

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Event Insertion Example

• Nodes A and B have claimed the same zone 0
• Node A generates event E lt0.4, 0.8, 0.9gt,
  code(E) 0
• Perimeter mode forwarding of event to B
• B and A engage in message exchange to shrink
  zones

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QueriesRouting and Resolving

• Routing for point queries same as event
• Range queries
• query initially routed to zone corresponding to
  the entire range
• progressively split into smaller sub-queries so
  each sub-query can be resolved by a single node

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QueriesSplitting Queries

• If the range of Qs first attribute contains
  value 0.5, A divides Q into two sub-queries, one
  with range 0 to 0.5, and the other 0.5 to 1
• If QA , part of zone A that overlaps with query
  area, is empty, A stops splitting
• Else A continues splitting the query using
  successive attribute ranges and recomputing QA
  until it is small enough to fit entirely in
  zone(A)

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QueriesSplitting Queries Example

• Suppose there is a node A with code(A) 0110
• Split a query Q lt0.3?0.8, 0.6?0.9gt

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QueryResolution

• Once a sub-query falls into a zone, the node
  owner resolves the query and sends the reply to
  the querier
• The other sub-queries are forwarded to other
  nodes

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Analysis on DIMs

• Metrics
• Average insertion cost average number of
  messages required to insert an event into the
  network
• Average query delivery cost average number of
  messages required to route a query message to all
  the relevant nodes
• Compared against alternatives
• GHT-R and flooding

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Average Insertion Cost
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Conclusion

• Under reasonable assumptions about query
  distributions, DIMs scale quite well with network
  size (both insertion and query costs scale O(vN))
• Work that still needs to be done
• Skewed data distribution
• Existential queries
• Node heterogeneity