Frugal: Building Degree-Constrained Overlay Topology from Social Graphs

Efficient and secure device to device communication is a necessary enabler for realization of fog and edge computing models. With an ever-increasing number, diversity, and geographical distribution of heterogeneous devices, ranging from pervasive sensor networks to edge cloudlets, the interconnection and network management of these devices emerges as a major challenge. Peer-to-peer (P2P) network overlays provide a scalable, decentralized and autonomous solution for interconnecting devices at the edge, and from the edge to the core of the cloud. This paper considers a networking system for edge computing that leverages trust embedded in online social networks (OSNs) to establish P2P overlays that offer the opportunity of private, authenticated device to device communications within the scope of a virtual private network (VPN). Mapping the social graph of OSNs onto an overlay network's topology presents challenges, since every social link that is mapped to an overlay has a cost associated with it, in terms of energy and resources consumed on link-setup and maintenance (especially for power-constrained devices). This paper addresses one key challenge in this context: dealing with high-degree social nodes. We propose a distributed mechanism - Frugal - that allows devices bound to a social user to make co-operative, but independent decisions to select social links to be mapped to overlay links. The approach leverages existing heuristics on computing minimum cost degree constrained spanning trees for graphs, but is novel in how it applies costs to graph edges using only local neighborhood information at each node, and how it operates in a distributed fashion. Simulation studies consider Frugal and two other policies (Greedy, Random) for capping the number of links in high-degree social nodes. Our simulation study carried out on social datasets indicates that significant degree reduction for high degree nodes/devices can be achieved without incurring major degradation in connectivity or performance loss in resulting overlay networks.