Computing on Anonymous Networks: Part I-Characterizing the Solvable Cases
IEEE Transactions on Parallel and Distributed Systems
Computing vector functions on anonymous networks
PODC '97 Proceedings of the sixteenth annual ACM symposium on Principles of distributed computing
Computing anonymously with arbitrary knowledge
Proceedings of the eighteenth annual ACM symposium on Principles of distributed computing
Self-stabilizing systems in spite of distributed control
Communications of the ACM
Discrete Mathematics
An Effective Characterization of Computability in Anonymous Networks
DISC '01 Proceedings of the 15th International Conference on Distributed Computing
Universal dynamic synchronous self-stabilization
Distributed Computing
Local and global properties in networks of processors (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
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It is known that computations of anonymous networks can be reduced to the construction of a certain graph, the minimum base of the network. The crucial step of this construction is the inference of the minimum base from a finite tree that each processor can build (its truncated view). We isolate those trees that make this inference possible, and call them holographic. Intuitively, a tree is holographic if it is enough self-similar to be uniquely extendible to an infinite tree. This possibility depends on a size function for the class of graphs under examination, which we call a holographic bound for the class. Holographic bounds give immediately, for instance, bounds for the quiescence time of self-stabilizing protocols. In this paper we give weakly tight holographic bounds for some classes of graphs.