Holographic trees

Abstract

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.