Effective storage capacity of labeled graphs

Authors:
Dana Angluin;James Aspnes;Rida A. Bazzi;Jiang Chen;David Eisenstat;Goran Konjevod
Affiliations:
Department of Computer Science, Yale University, United States;Department of Computer Science, Yale University, United States;Computer Science and Engineering, SCIDSE, Arizona State University, United States;Google, United States;Department of Computer Science, Brown University, United States;Lawrence Livermore National Laboratory, United Sates
Venue:
Information and Computation
Year:
2014

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Abstract

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. Specifically, we are interested in 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 is related to the information-theoretic capacity which we introduce in the paper. It equals the information-theoretic capacity of the graph up to constant factors for trees, random graphs with polynomial edge probabilities, and bounded-degree graphs.