Self‐Organising Sensors for Wide Area Surveillance using the Max‐Sum Algorithm Alex Rogers and Nick Jennings School of Electronics and Computer Science University of Southampton Alessandro Farinelli Department of Computer Science University of Verona Verona, Italy

Overview Self-Organisation –Landscape of Decentralised Coordination Algorithms Local Message Passing Algorithms –Max-sum algorithm –Graph Colouring Wide Area Surveillance Scenario Future Work

Self-Organisation Sensors

Self-Organisation Agents Multiple conflicting goals and objectives Discrete set of possible actions

Self-Organisation Agents Multiple conflicting goals and objectives Discrete set of possible actions Some locality of interaction

Self-Organisation Agents Maximise Social Welfare: Multiple conflicting goals and objectives Discrete set of possible actions Some locality of interaction

Self-Organisation Agents Central point of control Decentralised self-organisation through local computation and message passing. Speed of convergence, guarantees of optimality, communication overhead, computability No direct communication Solution scales poorly Central point of failure Who is the centre?

Landscape of Algorithms Complete Algorithms DPOP OptAPO ADOPT Communication Cost Optimality Iterative Algorithms Best Response (BR) Distributed Stochastic Algorithm (DSA) Fictitious Play (FP) Message Passing Algorithms Sum-Product Algorithm

Max-Sum Algorithm Variable nodes Function nodes Factor Graph A simple transformation: allows us to use the same algorithms to maximise social welfare: Find approximate solutions to global optimisation through local computation and message passing:

Graph Colouring Agent function / utility variable / state Graph Colouring ProblemEquivalent Factor Graph

Graph Colouring Equivalent Factor Graph Utility Function

Graph Colouring

Optimality

Communication Cost

Robustness to Message Loss

Wide Area Surveillance Scenario Dense deployment of sensors to detect pedestrian and vehicle activity within an urban environment. Unattended Ground Sensor

Energy Constrained Sensors Maximise event detection whilst using energy constrained sensors: –Use sense/sleep duty cycles to maximise network lifetime of maintain energy neutral operation. –Coordinate sensors with overlapping sensing fields. time duty cycle t ime duty cycle

Self-Organising Sensor Network

Energy-Aware Sensor Networks

Future Work Continuous action spaces –Max-sum calculations are not limited to discrete action space –Can we perform the standard max-sum operators on continuous functions in a computationally efficient manner? Bounded Solutions –Max-sum is optimal on tree and limited proofs of convergence exist for cyclic graphs –Can we construct a tree from the original cyclic graph and calculate an lower bound on the solution quality?