| Summary: | We present methods for distributed self-assembly that utilize simple rule-of-thumb control and communication schemes providing probabilistic performance guarantees. These methods represents a staunch departure from existing approaches that require more sophisticated control and communication, but provide deterministic guarantees. In particular, we show that even under severe communication restrictions, any assembly described by an acyclic weighted graph can be assembled with a rule set that is linear in the number of nodes contained in the desired assembly graph. We introduce the concept of stochastic
stability to the self-assembly problem and show that stochastic stability of desirable configurations can be exploited to provide probabilistic performance guarantees for the process. Relaxation of the communication restrictions allows simple approaches giving deterministic guarantees. We establish a clear relationship between availability of communication and convergence properties. We consider Self-assembly tasks for the cases of many and few
agents as well as large and small assembly goals. We analyze sensitivity of the presented process to communication errors as well as ill-intentioned agents. We discuss convergence rates of the presented process and directions for improving them.
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