Physarum-Inspired Self-biased Walkers for Distributed Clustering

We propose a distributed scheme to compute distance-based clusters. We first present a mechanism based on the flow of distributed tokens called walkers, circulating randomly between a source and a sink to compute a shortest path. Each time a walker takes an edge, it reinforces the probability that subsequent walkers take it. This mechanism is a discrete emulation of the slime mould (

Physarum polycephalum

) dynamics presented in [16]: each node observes the flow of walkers going through each adjacent edge and uses this flow to compute the probabilities with which it sends the walkers through each edge. Then, based on this mechanism, we show how several sources compute a shortest path DAG to a given sink. Finally, given some clusterheads acting like sinks, we show that this process converges to distance-based clusters (i.e. nodes join the clusterhead to which they are closest) with shortest-path DAGs. The algorithm is designed with a special focus on dynamic networks: the flow locally adapts to the appearance and disappearance of links and nodes, including clusterheads.