Storage Capacity of Labeled Graphs

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.

• Type: Journal
• Year: 2010
• Where: SSS
• Authors: Dana Angluin, James Aspnes, Rida A. Bazzi, Jiang Chen, David Eisenstat, Goran Konjevod
• Keywords: Connected Undirected Graph, Control Systems, Exact Information-theoretic Bound, Information-theoretic Capacity, SSS 2010