A Decentralised Coordination Algorithm for Maximising Sensor Coverage in Large Sensor Networks Ruben...
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A Decentralised Coordination Algorithm for Maximising Sensor Coverage in
Large Sensor NetworksRuben Stranders, Alex Rogers and Nicholas R. Jennings
School of Electronics and Computer ScienceUniversity of Southampton, UK
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This work is about constructing large sensor networks
Frequency assignment problem
Maintain good sensor quality
Efficient (polynomial time) algorithms
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These networks consist of many resource constrained sensing devices
2. Construct communication network
Radio Link
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Sensing quality is modelled by a submodular set function
Q({1, 3}) – Q({1}) ≥ Q({1, 2, 3}) – Q({1, 2})Models the diminishing returns of adding a sensor
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Sensing quality is modelled by a submodular set function
Examples (Guestrin 2005):• Mutual Information• Area Coverage• Entropy
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Frequency allocation is one of the key challenges
Equivalent to (multi-agent) graph colouring
Communication graph
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Frequency allocation is one of the key challenges
Garbled Reception
Colouring the communication graph is not sufficient
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Frequency allocation is one of the key challenges
We need to consider the conflict graph(Square of the communication graph)
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Frequency allocation is one of the key challenges
We need to consider the conflict graph(Square of the communication graph)
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The frequency allocation is one of the key challenges
Multi-agent graph colouring occurs often in sensor networkse.g. Coordination of sense/sleep cycles
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Frequency allocation is a difficult challenge for two reasons
1. Might need many frequencies
Reduced bandwidth
2. NP-hard problem Poor approximationsRequires lots of resources
or
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Specifically, our approach is to make the communication graph triangle-free
Colourable with threecolours
Colouring can be foundin linear time
Might need many colours
Colouring is NP-hard
Arbitrary Graph Triangle-free Graph(K3-minor free)
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Specifically, our approach is to make the communication graph triangle-free
Colourable with threecolours
Colouring can be foundin linear time
Might need many colours
Colouring is NP-hard
Arbitrary Graph Triangle-free Graph(K3-minor free)
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Specifically, our approach is to make the communication graph triangle-free
Triangle-free Graph(K3-minor free)
Colourable with threecolours
Colouring can be foundin linear time
Specifically, our approach is to make the communication graph triangle-free
Colourable with threecolours
Colouring can be foundin linear time
Triangle-free Graph(K3-minor free)
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Colourable with sixcolours
Colouring is easy
Square of Triangle-free Graph
Communication Graph
Conflict Graph
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However, by deactivating sensors, we lose sensing quality
Sensing quality is given by submodular function
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Maximising quality while simplifying frequency allocation is still NP-hard
Maximise sensing quality subject to graph being triangle-free
Maximising submodular function subject to p-independence constraint
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The centralised algorithm iteratively selects sensors that improve quality
• Creating a triangle
Each iteration, activate the sensor that:
without
• Maximises quality increase
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The algorithm terminates when no remaining sensor can be activated
Can’t add:creates triangle!
Can’t select any more sensors.
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The algorithm terminates when no remaining sensor can be activated
DoneCan’t select any more sensors.
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The centralised algorithm achieves at least 1/7th of the optimal quality
This follows from submodularity and p-independence
Greedy Optimal
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The centralised algorithm achieves at least 1/7th of the optimal quality
p-independence system
Need to remove at most p sensors after adding an arbitrary sensor to retain triangle-freeness
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The centralised algorithm achieves at least 1/7th of the optimal quality
p-independence system
Need to remove at most p sensors after adding an arbitrary sensor to retain triangle-freeness
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The centralised algorithm achieves at least 1/7th of the optimal quality
p-independence system
Need to remove at most p sensors after adding an arbitrary sensor to retain triangle-freeness
p = 6
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The centralised algorithm achieves at least 1/7th of the optimal quality
Greedily maximising submodular function
subject to p-independence constraint
QG ≥ 1/(1+p) Q*
QG ≥ 1/7 Q*
(Nemhauser, 1978)
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Using similar techniques, we created a decentralised algorithm
In every triangle deactivate the sensor that blocks the two with highest quality
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Central Idea
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Using similar techniques, we created a decentralised algorithm
Sensors activate themselves asynchronously 1 2
3 4
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Sensor checks if it is part of a triangle
Sensors check if activating themselves block sensors with higher quality
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3 4
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Sensors check if activating themselves block sensors with higher quality
Is the sensor part of a triangle?
Yes: we have to deactivate at least one of these
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3 4No: the sensor can remain active
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Sensor checks if its contribution is smaller than that of the other two
Q({1, 2}) ≤ Q({2, 3})
Q({1, 3}) ≤ Q({2, 3})and
Sensors check if activating themselves block sensors with higher quality
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3 4
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and✓
✓
Sensors check if activating themselves block sensors with higher quality
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Q({1, 2}) ≤ Q({2, 3})
Q({1, 3}) ≤ Q({2, 3})
Sensor checks if its contribution is smaller than that of the other two
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If so, it deactivates itself
Sensors check if activating themselves block sensors with higher quality
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3 4
Sensor checks if its contribution is smaller than that of the other two
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and✘
✓
Sensors check if activating themselves block sensors with higher quality
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3 4
Q({2, 3}) ≤ Q({3, 4})
Q({2, 4}) ≤ Q({3, 4})
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To evaluate the algorithms, we simulated sensor deployments
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Unit squareenvironment
R300 sensors
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Both algorithms provide >70% sensing quality of the original deployment
0.1 0.2 0.3 0.4 0.50.600000000000001
0.700000000000001
0.800000000000001
0.900000000000001
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OptimalCentralisedDecentralised
Loss from restricting solution( < 20% )
Loss from suboptimalsolution( < 10% )
Sens
ing
Qua
lity
Sensing Radius
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We also considered a dynamic environment, where sensors can fail
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R
When a sensor fails:
Centralised: rerun algorithm with remaining sensors
Decentralised: rerun algorithm if a neighbour fails
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Both algorithms achieve a coverage over time close to the optimal
0.10 0.20 0.30 0.40 0.500
500
1000
1500One at a timeCentralisedDecentralisedAll active
Cove
rage
x T
ime
Sensing Radius
Upper bound on achievable performance