Optimizing sensors placement in complex networks for localization of hidden signal source: A review

Abstract

As the world becomes more and more interconnected, our everyday objects become part of the Internet of Things, and our lives get more and more mirrored in virtual reality, where every piece of information, including misinformation, fake news and malware, can spread very fast practically anonymously. To suppress such uncontrolled spread, efficient computer systems and algorithms capable to track down such malicious information spread have to be developed. Currently, the most effective methods for source localization are based on sensors which provide the times at which they detect the spread. We investigate the problem of the optimal placement of such sensors in complex networks and propose a new graph measure, called Collective Betweenness, which we compare against four other metrics. Extensive numerical tests are performed on different types of complex networks over the wide ranges of densities of sensors and stochasticities of signal. In these tests, we discovered clear difference in comparative performance of the investigated optimal placement methods between real or scale-free synthetic networks versus narrow degree distribution networks. The former have a clear region for any given method’s dominance in contrast to the latter where the performance maps are less homogeneous. We find that while choosing the best method is very network and spread dependent, there are two methods that consistently stand out. High Variance Observers seem to do very well for spread with low stochasticity whereas Collective Betweenness, introduced in this paper, thrives when the spread is highly unpredictable.