A computationally-efficient sandbox algorithm for multifractal analysis of large-scale complex networks with tens of millions of nodes
Yuemin Ding, Jin-Long Liu, Xiaohui Li, Yu-Chu Tian, Zu-Guo Yu

TL;DR
This paper introduces a new computationally-efficient sandbox algorithm (CESA) for multifractal analysis of large-scale complex networks, significantly reducing time and space complexity to enable analysis of networks with tens of millions of nodes.
Contribution
The paper presents CESA, a novel sandbox MFA algorithm that employs BFS and sparse data structures to improve efficiency for large-scale networks.
Findings
CESA reduces time complexity from cubic to quadratic.
CESA decreases space complexity from quadratic to linear.
CESA successfully analyzes real-world networks with tens of millions of nodes.
Abstract
Multifractal analysis (MFA) is a useful tool to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. One of the widely used methods for fractal analysis is box-covering. It is known to be NP-hard. More severely, in comparison with fractal analysis algorithms, MFA algorithms have much higher computational complexity. Among various MFA algorithms for complex networks, the sandbox MFA algorithm behaves with the best computational efficiency. However, the existing sandbox algorithm is still computationally expensive. It becomes challenging to implement the MFA for large-scale networks with tens of millions of nodes. It is also not clear whether or not MFA results can be improved by a largely increased size of a theoretical network. To tackle these challenges, a computationally-efficient sandbox algorithm (CESA) is presented in this paper…
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