Solving the speed and accuracy of box-covering problem in complex networks

Abstract

The box-covering method that covers a network with a minimum number of boxes is critical to demonstrate network fractals and the re-normalization analysis of complex networks. Moreover, one is able to investigate the network structure by analyzing the re-normalization flow or categorizing networks into several universal classes. A number of compelling methods are not well adapted to the large-scale networks due to high time complexity, or low accuracy. In this paper, we introduce a hybrid method that has high accuracy and low time consumption based the maximum-excluded-mass-burning (MEMB) method and the random sequential (RS) method. Our method combines the characteristics of the MEMB method that search as fewer boxes as possible with the high efficiency of the RS method by selecting a few unimportant central nodes, especially for large-scale networks. We also optimize the storage mechanism of the method so that the excluded mass of nodes can be updated efficiently. Experiments in the real networks with different structures demonstrate that the improvement of our method can be substantial. Our method reduces the time consumption of the MEMB method by more than 40% with only 10% more boxes than the MEMB method.