Wireless Distributed Sensor Tracking: Computation and Communication

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Wireless Distributed Sensor Tracking Computation
and Communication

• Bart Selman, Carla Gomes, Scott Kirkpatrick,
• Ramon Bejar, Bhaskar Krishnamachari,
• Johannes Schneider
• Intelligent Information Systems Institute,
  Cornell University Hebrew University
• Autonomous Negotiating Teams
  Principal Investigators'
  Meeting, Oct. 19, 2001

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Outline

• Overview of our approach
• Ants - Challenge Problem (Sensor Domain)
• Graph Models
• Results on average case complexity
• Distributed CSP model
• Phase Transitions --- 3D view (communication
• vs. complexity vs. overall performance)
• Conclusions and Future Work

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Overview of Approach

• Overall theme --- exploit impact of structure on
  computational complexity
• Identification of domain structural features
• tractable vs. intractable subclasses
• phase transition phenomena
• backbone
• balancedness
• Goal
• Use findings in both the design and operation of
  distributed platform
• Principled controlled hardness aware systems

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ANTs Challenge Problem
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• Multiple doppler radar sensors track moving
• targets
• Energy limited sensors
• Communication
• constraints
• Distributed
• environment
• Dynamic problem

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Domain Models
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• Start with a simple graph model
• Successively refine the model in stages to
• approximate the real situation
• Static weakly-constrained model
• Static constraint satisfaction model with
  communication constraints
• Static distributed constraint satisfaction model
• Dynamic distributed constraint satisfaction model
• Goal Identify and isolate the sources of
• combinatorial complexity

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Initial Assumptions
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• Each sensor can only track one target at a time
• 3 sensors are required to track a target

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Initial Graph Model
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• Bipartite graph G (S U T, E)
• S is the set of sensor nodes, T the set of
  target nodes, E the edges indicating which
  targets are visible to a given sensor
• Decision Problem Can each target be tracked by
  three sensors?

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Initial Graph Model
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Initial Graph Model

• The initial model presented is a bipartite
  graph, and this problem can be solved using a
  maximum flow algorithm in polynomial time
• Results incorporated into framework developed
  by Milind Tambes group at ISI, USC
• Joint work in progress

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Sensor Communication Constraints

• In the graph model, we now have additional edges
  between sensor nodes

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Constrained Graph Model
sensors
targets
communication links
possible solution
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• Complexity and Phase Transition Phenomena

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Worst-Case Complexity
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• Decision Problem Can each target be
• tracked by three sensors which can
• communicate together ?
• We have shown that this constraint
• satisfaction problem (CSP) is NP-
• complete, by reduction from the
• problem of partitioning a graph into
• isomorphic subgraphs

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• What about average- case complexity?

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Description of Experiments
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Description of Experiments
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• Limit cases

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Phase Transition w.r.t. Communication Range
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Experiments with a configuration of 9 sensors and
3 targets such that there is a communication
channel between two sensors with probability p
Insights into the design and operation of sensor
networks w.r.t. communication range
Probability( all targets tracked )
Special case all targets are visible to all
sensors
Communication edge probability p
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Phase Transition w.r.t. Radar Detection Range
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Experiments with a configuration of 9 sensors and
3 targets such that each sensor is able to detect
targets within a range R
Insights into the design and operation of sensor
networks w.r.t. radar detection range
Probability( all targets tracked )
Special case all nodes can communicate
Normalized Radar Range R
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Communication vs. Radar Range vs. Performance

• The full picture

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Communication vs. Radar Range vs. Performance
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Radar range R from 0 (no target is covered) to 1
(all targets covered) Comm. range C from 0 (no
sensors communicates) to 1 (all sensors comm.)
Probability of tracking all targets
5 targets, 15 sensors
5 targets, 17 sensors
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Distributed Computational Model
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• In a Distributed Constraint Satisfaction
• Problem (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
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• 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 target

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DCSP Models
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• With the DCSP models, we study both per-node
  computational costs as well as inter-node
  communication costs
• DCSP algorithms DIBT (Hamadi et al.) and ABT
  (Yokoo et al.)

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

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

Inter-agent constraints gt All sensors seeing a
target must know which sensors are tracking the
target
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Comparison of the two models
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Model Sensor-centered Target-centered
Agents Vars for intra constraints Vars for inter constraints Intra-agent constraints Inter-agent constraints Sensors Targets Targets Only one target 3 comm. sensors Targets Sensors -- 3 comm. sensors Only one target
Sensor-centered To check the inter-agent
constraints, sensors must maintain one variable
for every target they can track, that indicates
which 3 sensors are tracking it Target-centered
Does not need additional variables for the
inter-agent constraints
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Communication vs. Radar Range vs. Computation
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• Computational Complexity total
• computation cost for all agents
• Communication Complexity total
• number of messages sent by all agents
• Communication range / Sensor (radar) range
• provides 3rd dimension.
• These measures can vary for the same
• problem when using different DCSP models

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Average Complexity (target-centered)
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Mean computational cost
Probability of Tracking
X 104

• 5 targets and 17 sensors

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Average Complexity (target-centered)
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Probability of Tracking
Mean communication cost
1000

• 5 targets and 17 sensors

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Implicit versus Explicit Constraints
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• Explicit constraint no two targets 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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• Future Work

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Structure
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• Further study structural issues as they
• occur in the Sensor domain e.g.
• effect of balancing
• backbone (insights into critical resources)
• refinement of phase transition notions
  considering additional parameters
• (concepts introduced in previous PI meeting)

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Dynamic DCSP Model
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• Further refinement of the model
• incorporate target mobility
• The graph topology changes with time
• What are the complexity issues when
• online distributed algorithms are
• used?

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Purely Local Computation Models
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• We are also exploring local computation
• methods for target tracking.
• (I.e. communication cannot be used
• for global computation.)
• We are drawing on an analogy to
• physical models.
• (energy function minimization approach)

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• Summary

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Summary
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• Introduced graph-based models capturing
• the ANTs challenge domain
• Results on the tradeoffs between
• Computation, Communication, Radar range,
• and Performance.
• Results enable a more principled and
• efficient design of distributed sensor
  networks.
• Extensions
• additional structural issues for the sensor
  domain
• complexity issues in distributed and dynamic
  settings

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Collaborations / Interactions

• ISI Analytic Tools to Evaluate Negotiation
• Difficulty
• Design and evaluation of SAT encodings for
  CAMERAs scheduling task.
• ISI DYNAMITE
• Formal complexity analysis DCSP model (e.g.,
  characterization of tractable subclasses).
• UMASS Scalable RT Negotiating Toolkit
• Analysis of complexity of negotiation protocols.

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The End
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