SensorCSP: distributed constraint satisfaction in a wireless sensor tracking system

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SensorCSP distributed constraint satisfaction in
a wireless sensor tracking system

• Ramon Bejar, Bhaskar Krishnamachari, Carla Gomes,
  Bart Selman
• Intelligent Information Systems Institute (IISI),
• Cornell University
• Distributed Constraint Reasoning Workshop
  IJCAI01, August
  4, 2001

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Outline

• SensorCSP problem description
• Graph model
• Worst-case computational complexity
• Phase transitions
• DCSP models for SensorCSP
• Average distributed complexity
• computational complexity
• communication complexity
• Implicit and explicit constraints in SensorCSP

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SensorCSP
IISI, Cornell University

• Multiple sensors tracking mobile nodes
• Communication constraints
• Distributed environment
• Dynamic problem

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Problem Description
IISI, Cornell University

• Sensors only can track mobiles within their
  radar distance
• Each sensor can only track one mobile
• Sensors can only communicate if they share a
  communication link
• Need 3 communicating sensors tracking each mobile

sensor
communication link
mobile
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SensorCSP Graph Model
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Captures the static view of the problem
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Worst-case complexity
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• Decision Problem Can each mobile be tracked by
  3 sensors which can communicate together ?
• This constraint satisfaction problem is
  NP-complete.
• Proof reduction from the problem of
  partitioning a graph into isomorphic subgraphs

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Polynomial Special Case
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Polynomial Special Case

• The model for this case is a bipartite graph,
  and this problem can be solved using a maximum
  flow algorithm in polynomial time

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Phase Transitions in SensorCSP
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Radar range from 0 (no mobile is covered) to 1
(all mobiles covered) Comm. range from 0 (no
sensor communicates) to 1 (all sensors
communicate)
Probability of obtaining a Solvable instance
5 mobiles, 15 sensors
5 mobiles, 17 sensors
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Phase Transition w.r.t. Communication Range
IISI, Cornell University
Experiments with random configurations of 9
sensors and 3 mobiles increasing only the
communication range
Here all mobiles are visible
Probability( all mobiles tracked )
Communication range
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Phase Transition w.r.t. Radar Detection Range
IISI, Cornell University
Experiments with random configurations of 9
sensors and 3 mobiles increasing only the radar
range
Here all nodes can communicate
Probability( all mobiles tracked )
Normalized Radar Range R
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Distributed CSP Models
IISI, Cornell University

• In a distributed CSP (DCSP) variables and
  constraints are distributed among multiple
  agents. It consists of
• A set of agents 1, 2, n
• A set of CSPs P1, P2, Pn , one for each agent
• There are intra-agent constraints and
  inter-agent constraints

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DCSP Models
IISI, Cornell University

• We can represent the sensor tracking problem as
  a DCSP using dual representations
• One with each sensor as a distinct agent
• One with a distinct tracker agent for each mobile

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DCSP Models
IISI, Cornell University

• With the DCSP models, we study both per-node
  computational costs as well as inter-node
  communication costs
• DCSP algorithm DIBT (Hamadi et al.) We are in
  the process of using other algorithms.

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Mobile Tracker Agents
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• Intra-agent constraints
• Each mobile must be tracked by 3 communicating
  sensors to which it is visible
• Inter-agent constraints
• No common sensors between mobiles

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Sensor Agents
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• Intra-agent constraints
• Sensor must track at most 1 visible mobile
• Inter-agent constraints
• 3 communicating sensors should track each mobile

Inter-agent constraints gt All sensors seeing a
mobile must know which sensors are tracking the
target
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Comparison of the two models
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Sensor-centered To check the inter-agent
constraints, sensors must maintain one variable
for every mobile they can track, that indicates
which 3 sensors are tracking it Mobile-centered
Does not need additional variables for the
inter-agent constraints
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Communication vs. Computational Complexity
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• Computational Complexity total computation cost
  for all agents
• Communication Complexity total number of
  messages sent by all agents
• These measures can vary for the same problem when
  using different DCSP models

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Average Complexity (Mobile-centered)
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Mean computational cost
Mean communication cost
X 105
5000

• 5 mobiles and 53 sensors (minimal number of
  sensors)
• Peaks in computational and communication
  complexity

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Average Complexity (Mobile-centered)
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Mean computational cost
Mean communication cost
X 104
1000

• 5 mobiles and 532 sensors
• More dominant peak in complexity

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Average Complexity (Mobile-centered)
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Mean computational cost
Mean communication cost
12000
1500

• 5 mobiles and 534 sensors
• More dominant peak in complexity

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Implicit versus Explicit Constraints
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• Explicit constraint no two mobiles can be
  tracked by same sensor (e.g. t2, t3 cannot share
  s4 and t1, t3 cannot share s9)
• Implicit constraint due to a chain of explicit
  constraints (e.g. implicit constraint between s4
  for t2 and s9 for t1 )

s1
s2
s3
s4
s5
s6
s7
s8
s9
t1
1
1
x
x
1
0
x
x
x
x
x
1
x
x
x
1
x
1
t2
x
x
x
1
0
x
x
1
1
t3
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Communication Cost for Implicit Constraints

• Explicit constraints can be resolved by direct
  communication between agents
• Resolving Implicit constraints may require long
  communication paths through multiple agents ?
  scalability problems

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Summary
IISI, Cornell University

• SensorCSP interesting challenging problem for
  DCSP
• Two key parameters determining solvable instances
  and complexity
• Dual representations with tradeoffs in the
  number of intra-agent and inter-agent constraints
  

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Future Work
IISI, Cornell University

• Compare the performance of DIBT with other
  systematic DCSP algorithms
• Compare the complexity of the mobile-centered
  with the sensor-centered models
• Study the effect of different structural
  properties in SensorCSP problem instances
• 
  
• Further refinement of the model incorporate
  mobile mobility gt dynamic version of the problem