The NP-hard Effectors problem on directed graphs is motivated by applications in network mining, particularly concerning the analysis of probabilistic information-propagation processes in social networks. In the corresponding model the arcs carry probabilities and there is a probabilistic diffusion process activating nodes by neighboring activated nodes with probabilities as specified by the arcs. The point is to explain a given network activation state as well as possible by using a minimum number of “effector nodes”; these are selected before the activation process starts. We correct, complement, and extend previous work from the data mining community by a more thorough computational complexity analysis of Effectors, identifying both tractable and intractable cases. To this end, we also exploit a parameterization measuring the “degree of randomness” (the number of ‘really’ probabilistic arcs) which might prove useful for analyzing other probabilistic network diffusion problems as well.
Bulteau, L., Fafianie, S., Froese, V., Niedermeier, R., & Talmon, N. (2017). The Complexity of Finding Effectors. Theory of Computing Systems, 60(2), 253–279. https://doi.org/10.1007/s00224-016-9670-8