The Complexity of Finding Effectors

TL;DR

This paper analyzes the computational complexity of the NP-hard EFFECTORS problem in probabilistic social network models, identifying tractable and intractable cases and introducing a parameter related to the degree of randomness.

Contribution

It provides a comprehensive complexity analysis of EFFECTORS, correcting previous work and introducing a new parameter to measure the problem's complexity.

Findings

Identifies tractable and intractable cases of EFFECTORS.

Introduces a parameter measuring the degree of randomness in the network.

Extends previous computational complexity results for probabilistic network diffusion.

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.