Storage Capacity Of Labeled Graphs
SSS'10: Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems(2010)
摘要
We consider the question of how much information can be stored by labeling the vertices of a connected undirected graph G using a constant-size set of labels, when isomorphic labelings are not distinguishable. An exact information-theoretic bound is easily obtained by counting the number of isomorphism classes of labelings of G, which we call the information-theoretic capacity of the graph. More interesting is the effective capacity of members of some class of graphs, the number of states distinguishable by a Turing machine that uses the labeled graph itself in place of the usual linear tape. We show that the effective capacity equals the information-theoretic capacity up to constant factors for trees, random graphs with polynomial edge probabilities, and bounded-degree graphs.
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关键词
effective capacity,information-theoretic capacity,bounded-degree graph,connected undirected graph,exact information-theoretic,random graph,isomorphic labelings,states distinguishable,Turing machine,constant factor,storage capacity
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