Adaptive Collective Responses to Local Stimuli in Anonymous Dynamic Networks

We develop a framework for self-induced phase changes in programmable matter in which a collection of agents with limited computational and communication capabilities can collectively perform appropriate global tasks in response to local stimuli that dynamically appear and disappear. Agents reside on graph vertices, where each stimulus is only recognized locally, and agents communicate via token passing along edges to alert other agents to transition to an Aware state when stimuli are present and an Unaware state when the stimuli disappear. We present an Adaptive Stimuli Algorithm that is robust to competing waves of messages as multiple stimuli change, possibly adversarially. Moreover, in addition to handling arbitrary stimulus dynamics, the algorithm can handle agents reconfiguring the connections (edges) of the graph over time in a controlled way. As an application, we show how this Adaptive Stimuli Algorithm on reconfigurable graphs can be used to solve the foraging problem, where food sources may be discovered, removed, or shifted at arbitrary times. We would like the agents to consistently self-organize, using only local interactions, such that if the food remains in a position long enough, the agents transition to a gather phase in which many collectively form a single large component with small perimeter around the food. Alternatively, if no food source has existed recently, the agents should undergo a self-induced phase change and switch to a search phase in which they distribute themselves randomly throughout the lattice region to search for food. Unlike previous approaches to foraging, this process is indefinitely repeatable, withstanding competing waves of messages that may interfere with each other. Like a physical phase change, microscopic changes such as the deletion or addition of a single food source trigger these macroscopic, system-wide transitions as agents share information about the environment and respond locally to get the desired collective response.