Upper Bound of Relative Error of Random Ball Coverage for Calculating Fractal Network Dimension

Least box number coverage problem for calculating dimension of fractal networks is a NP-hard problem. Meanwhile, the time complexity of random ball coverage for calculating dimension is very low. In this paper we strictly present the upper bound of relative error for random ball coverage algorithm. We also propose twice-random ball coverage algorithm for calculating network dimension. For many real-world fractal networks, when the network diameter is sufficient large, the relative error upper bound of this method will tend to 0. In this point of view, given a proper acceptable error range, the dimension calculation is not a NP-hard problem, but P problem instead.