A Decentralised Coordination Algorithm for Maximising Sensor Coverage in Large Sensor
NetworksRuben Stranders, Alex Rogers and Nicholas R. Jennings
Intelligence, Agents, Multimedia Group, School of Electronics and Computer Science, University of SouthamptonProblem DescriptionFrequency allocation in sensor networks consisting of many sensors is a difficult challenge and is equivalent to (multi-agent) graph colouring
Our ApproachSimplify the communication graph by deactivating sensors, and solve the frequency assignment problem in the new graph
Arbitrary Graph Triangle-free Graph
Specifically, we make the communication graph Triangle-free (No 3-cliques)
Colourable with three colours
Colouring can be found in O(n)Needs many colours
Colouring is NP-hard
However, by deactivating we reduce the sensing quality of the sensor network!
How to maximise sensor quality subject to the communication graph being triangle-free?
A Centralised Greedy AlgorithmCentral idea: Iteratively select sensors that improve quality the most, while keeping communication graph triangle-free.
Example:
Original deployment Step 1 Step 2: Termination
A Decentralised Greedy AlgorithmThe Model
On random activation
1 2
3 4
Adding any sensor will introduce triangle
Problem is NP-hard for arbitrary graphs
Problem ConsequenceMany frequencies needed, resulting in low bandwidth
Chromatic number is high
Poor approximationsComputationally expensive
or
Equivalent problem: scheduling sensor activation cycles
Does a triangle (A, B, C) exist?
Q({A, B}) < Q ({B, C})and
Q({A, C}) < Q ({B, C})
Sensor 1 active
Q(1, 2) < Q (2, 3) Q(1, 3) < Q (2, 3)
Sensor 1 deactivates
Sensor is member of triangle (1, 2, 3)
Deactivate
Stay active
no
yesyesno
Central idea: deactivate sensors that block sensors with higher quality
Example:
1 2
3 4
1 2
3 4
Sensor 2 active
Q(2, 3) > Q (3, 4) Q(2, 4) < Q (3, 4)
Sensor is member of triangle (2, 3, 4)
Wait for next activation
1 2
3 4
The final result is the same as that of the centralised algorithm above
0.1 0.2 0.3 0.4 0.50.600000000000001
0.700000000000001
0.800000000000001
0.900000000000001
1
OptimalCentralisedDecentralised
Loss from restricting solution( <20% )Loss from suboptimalsolution( <10% )
Sen
sing
Qua
lity
(frac
tion
of o
rigin
al)
Sensing Radius (fraction of deployment area length)
Empirical Results
Q({1, 3}) – Q({1}) ≥ Q({1, 2, 3}) – Q({1, 2})
3
1
3
12
Key Challenge
The sensing quality of the network is given by a submodular set function Q, which captures diminishing returns of adding sensors
Example:
The communication graph represents which sensors can communicate. Connected sensors need to use different frequencies to prevent garbled transmissions.
CommunicationLink
Sensor
Our (de)centralised algorithms create sensor networks with high sensor quality and a simplified communication network, making the frequency assignment problem tractable.
Conclusion
Moreover, a ε-greedy algorithm found a colouring in >>1000 instances