Selected Problems in Data Driven and Traffic Related Networks

In our research we concentrate on networks. The topic of networks has been extensively studied over the last few decades and it is still gaining popularity. In this thesis we study the challenge of gaining an understanding of networks when information about the network is unknown or limited in some way. Initially we consider the challenge of understanding from a vast amount of information what can be used to provide insight into the behaviour of the network, and for this we consider methods and techniques adopted from the social network analysis (SNA) community. Following this, we consider networks that have access to data that is limited in some way and demonstrate that statistical analysis methods can be used to overcome these challenges. Finally, we consider the challenge of having exposure to increasingly less information about the network, and we demonstrate this difficulty by considering the rendezvous problem in a restricted network

Asynchronous rendezvous with different maps

© Springer Nature Switzerland AG 2019. This paper provides a study on the rendezvous problem in which two anonymous mobile entities referred to as robots rA and rB are asked to meet at an arbitrary node of a graph G = (V,E). As opposed to more standard assumptions robots may not be able to visit the entire graph G. Namely, each robot has its own map which is a connected subgraph of G. Such mobility restrictions may be dictated by the topological properties combined with the intrinsic characteristics of robots preventing them from visiting certain edges in E. We consider four different variants of the rendezvous problem introduced in [Farrugia et al. SOFSEM’15] which reflect on restricted maneuverability and navigation ability of rA and rB in G. In the latter, the focus is on models in which robots’ actions are synchronised. The authors prove that one of the maps must be a subgraph of the other. I.e., without this assumption (or some extra knowledge) the rendezvous problem does not have a feasible solution. In this paper, while we keep the containment assumption, we focus on asynchronous robots and the relevant bounds in the four considered variants. We provide some impossibility results and almost tight lower and upper bounds when the solutions are possible