### Abstract

Covering a network with the minimum possible number of boxes can reveal interesting features for the network structure, especially in terms of self-similar or fractal characteristics. Considerable attention has been recently devoted to this problem, with the finding that many real networks are self-similar fractals. Here we present, compare and study in detail a number of algorithms that we have used in previous papers towards this goal. We show that this problem can be mapped to the well-known graph colouring problem and then we simply can apply well-established algorithms. This seems to be the most efficient method, but we also present two other algorithms based on burning which provide a number of other benefits. We argue that the algorithms presented provide a solution close to optimal and that another algorithm that can significantly improve this result in an efficient way does not exist. We offer to anyone that finds such a method to cover his/her expenses for a one-week trip to our lab in New York (details in http://jamlab.org).

Original language | English (US) |
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Article number | P03006 |

Journal | Journal of Statistical Mechanics: Theory and Experiment |

Issue number | 3 |

DOIs | |

State | Published - Mar 1 2007 |

Externally published | Yes |

### Keywords

- Analysis of algorithms
- Growth processes

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Statistics, Probability and Uncertainty

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## Cite this

*Journal of Statistical Mechanics: Theory and Experiment*, (3), [P03006]. https://doi.org/10.1088/1742-5468/2007/03/P03006