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Least box number coverage problem for calculating dimension of fractalnetworks is a NP-hard problem. Meanwhile, the time complexity of random ballcoverage for calculating dimension is very low. In this paper we strictlypresent the upper bound of relative error for random ball coverage algorithm.We also propose twice-random ball coverage algorithm for calculating networkdimension. For many real-world fractal networks, when the network diameter issufficient 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 dimensioncalculation is not a NP-hard problem, but P problem instead.

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