Computational aspects of optimal strategic network diffusion

Abstract

The diffusion of information has been widely modeled as stochastic diffusion processes on networks. Alshamsi et al.[1] proposed a model of strategic diffusion in networks of related activities. In this work we investigate the computational aspects of finding the optimal strategy of strategic diffusion. We prove that finding an optimal solution to the problem is NP-complete in a general case. To overcome this computational difficulty, we present an algorithm to compute an optimal solution based on a dynamic programming technique. We also show that the problem is fixed parameter-tractable when parametrized by the product of the treewidth and maximum degree. We analyze the possibility of developing an efficient approximation algorithm and show that two heuristic algorithms proposed so far cannot have better than a logarithmic approximation guarantee. Finally, we prove that the problem does not admit better than a logarithmic approximation, unless P=NP. arXiv:1809.03141v1 [cs.CC]

The policy implications of economic complexity

“…When approaches were introduced recently by Alshamsi et al ( 2018) (expanded theoretically in Waniek et al (2020)). Unlike most work on relatedness, which tends to be statistical, Alshamsi's work starts by accepting relatedness as an empirical fact and building mathematical models to explore the question: what is the optimal strategy to diversify an economy?…”

“…3 b is still an open question. While this shape can be determined analytically in trivial cases, such as highly symmetric toy models (Alshamsi et al, 2018), determining it for more complex topologies is a more challenging numerical exercise, and technically, and NP-complete problem (Waniek et al, 2020).…”