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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 Frequency allocation in sensor networks consisting of many sensors is a difficult challenge and is equivalent to (multi-agent) graph colouring Our Approach Simplify 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 Algorithm Central 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 Algorithm The Model On random activati on 1 2 3 4 Adding any sensor will introduce triangle Problem is NP-hard for arbitrary graphs Problem Consequence Many frequencies needed, resulting in low bandwidth Chromatic number is high Poor approximations Computationally 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) Deactiva te Stay active no yes yes no 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 0.5 0.600000000000001 0.700000000000001 0.800000000000001 0.900000000000001 1 Optimal Centralised Decentralised Loss from restrictin g solution ( <20% ) Loss from suboptimal solution ( <10% ) Sensing Quality (fraction of original) Sensing Radius (fraction of deployment area length) Empirical Results Q({1, 3}) – Q({1}) ≥ Q({1, 2, 3}) – Q({1, 2}) 3 1 3 1 2 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. Communication Link 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
