Adaptive collective responses to local stimuli in anonymous dynamic networks

Abstract

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 are represented by vertices in a dynamic graph $G$ whose edge set changes over time, and stimuli are placed adversarially on the vertices of $G$ where each agent is only capable of recognizing a co-located stimulus. 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 can handle arbitrary adversarial stimulus dynamics, while an adversary (or the agents themselves) reconfigures the connections (edges) of $G$ over time in a controlled way. This algorithm can be used to solve the foraging problem on reconfigurable graphs where, in addition to food sources (stimuli) being discovered, removed, or shifted arbitrarily, 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 collective phase change and switch to a search phase in which they distribute themselves randomly throughout the graph to search for food. Unlike previous approaches to foraging, this process is indefinitely repeatable, withstanding competing broadcast waves of state transition that may interfere with each other. Like a physical phase change, such as the ferromagnetic models underlying the gather and search algorithms used for foraging, microscopic changes in the environment trigger these macroscopic, system-wide transitions as agents share information and respond locally to get the desired collective response.