  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 coloring 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 presented
algorithms 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 1-week
trip to our lab in New York (details in http://jamlab.org).
