Chaoming Song et al J. Stat. Mech. (2007) P03006 doi:10.1088/1742-5468/2007/03/P03006
Chaoming Song1, Lazaros K Gallos1, Shlomo Havlin2 and Hernán A Makse1
Show affiliationsCovering 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).
02.10.Ox Combinatorics; graph theory
Issue 03 (March 2007)
Received 11 December 2006, accepted for publication 11 February 2007
Published 5 March 2007
Chaoming Song et al J. Stat. Mech. (2007) P03006
Toshiaki Iida and Miki Wadati J. Stat. Mech. (2007) P06011
M Caselle et al J. Stat. Mech. (2004) P10009
Pasquale Calabrese and John Cardy J. Stat. Mech. (2007) P06008
Andreas M Läuchli et al J. Stat. Mech. (2008) P01010
Yoshiyuki Y Yamaguchi et al J. Stat. Mech. (2007) P01020
M T Batchelor et al J. Stat. Mech. (2005) L10001
Anthony Longjas et al J. Stat. Mech. (2009) P05006
R Flume and A Klitz J. Stat. Mech. (2008) N10001
Giulio Biroli et al J. Stat. Mech. (2007) P07019