Network Parameters in Practice: A Case Study Using the Target Set Selection Problem

It is well known that many real-world networks (`complex´ networks), such as social, biological, and communication networks, have distinctive topological features. However, in general, it is an open question whether or not these features can provide any algorithmic benefits. In this paper we introduce ideas from the area of parameterized complexity to try and provide a partial answer to this question. We investigate the values of some of the parameters commonly employed by the parameterized complexity community in a range of real social, biological, and communication networks. In all cases, the parameter values are much too high to be of practical use. We then investigate dynamic strategies for exploiting the distinctive topological features of real-world networks to improve the prospects for efficient computation of acceptable problem solutions, using both fixed-parameter and greedy approaches. Our strategies involve simple targeted operations, vertex deletion and edge addition, that could easily be applied in the case of social networks, for example. As a case study, we consider the Target Set Selection problem, a general and ubiquitous problem that models many problems concerning the spread of information in networks.