### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 44-56 |

Number of pages | 13 |

Journal | Information and Computation |

Volume | 234 |

DOIs | |

State | Published - Feb 2014 |

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### ASJC Scopus subject areas

- Information Systems
- Computational Theory and Mathematics
- Theoretical Computer Science
- Computer Science Applications

### Cite this

*Information and Computation*,

*234*, 44-56. https://doi.org/10.1016/j.ic.2013.11.004

**Effective storage capacity of labeled graphs.** / Angluin, Dana; Aspnes, James; Bazzi, Rida; Chen, Jiang; Eisenstat, David; Konjevod, Goran.

Research output: Contribution to journal › Article

*Information and Computation*, vol. 234, pp. 44-56. https://doi.org/10.1016/j.ic.2013.11.004

}

TY - JOUR

T1 - Effective storage capacity of labeled graphs

AU - Angluin, Dana

AU - Aspnes, James

AU - Bazzi, Rida

AU - Chen, Jiang

AU - Eisenstat, David

AU - Konjevod, Goran

PY - 2014/2

Y1 - 2014/2

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84894268389&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894268389&partnerID=8YFLogxK

U2 - 10.1016/j.ic.2013.11.004

DO - 10.1016/j.ic.2013.11.004

M3 - Article

VL - 234

SP - 44

EP - 56

JO - Information and Computation

JF - Information and Computation

SN - 0890-5401

ER -