A Decentralised Coordination Algorithm for Maximising Sensor Coverage in Large Sensor Networks

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