Probabilistic Performance Guarantees for Distributed Self-Assembly


In distributed self-assembly, a mess of agents ask for to form copies of a specific structure, modeled here as a labeled graph. In the model, agents encounter every different in spontaneous pairwise interactions and judge whether or not or not to form or sever edges based mostly on their two labels and a fastened set of local interaction rules described by a graph grammar. The target is to converge on a graph with a maximum range of copies of a given target graph. Our main result is the introduction of a easy algorithm that achieves an asymptotically most yield in a probabilistic sense. Notably, agents don't want to update their labels except when forming or severing edges. This contrasts with sure existing approaches that exploit information propagating rules, effectively addressing the choice drawback at the amount of subgraphs versus individual vertices. We tend to will be able to obey a lot of stringent locality requirements while also providing smaller rule sets. The results will be improved upon if sure requirements on the labels are relaxed. We discuss limits of performance in self-assembly in terms of rule set characteristics and achievable maximum yield.

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