The Complexity of Finding Effectors

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Abstract

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.

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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

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