Spatial networks with wireless applications

Many networks have nodes located in physical space, with links more common between closely spaced pairs of nodes. For example, the nodes could be wireless devices and links communication channels in a wireless mesh network. We describe recent work involving such networks, considering effects due to the geometry (convex,non-convex, and fractal), node distribution, distance-dependent link probability, mobility, directivity and interference.Comment: Review article- an amended version with a new title from the origina

Communication Over a Wireless Network With Random Connections

A network of nodes in which pairs communicate over a shared wireless medium is analyzed. We consider the maximum total aggregate traffic flow possible as given by the number of users multiplied by their data rate. The model in this paper differs substantially from the many existing approaches in that the channel connections in this network are entirely random: rather than being governed by geometry and a decay-versus-distance law, the strengths of the connections between nodes are drawn independently from a common distribution. Such a model is appropriate for environments where the first-order effect that governs the signal strength at a receiving node is a random event (such as the existence of an obstacle), rather than the distance from the transmitter. It is shown that the aggregate traffic flow as a function of the number of nodes n is a strong function of the channel distribution. In particular, for certain distributions the aggregate traffic flow is at least n/(log n)^d for some d≫0, which is significantly larger than the O(sqrt n) results obtained for many geometric models. The results provide guidelines for the connectivity that is needed for large aggregate traffic. The relation between the proposed model and existing distance-based models is shown in some cases

A Comprehensive Survey of Potential Game Approaches to Wireless Networks

Potential games form a class of non-cooperative games where unilateral improvement dynamics are guaranteed to converge in many practical cases. The potential game approach has been applied to a wide range of wireless network problems, particularly to a variety of channel assignment problems. In this paper, the properties of potential games are introduced, and games in wireless networks that have been proven to be potential games are comprehensively discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on Communications, vol. E98-B, no. 9, Sept. 201

Quantifying Link Stability in Ad Hoc Wireless Networks Subject to Ornstein-Uhlenbeck Mobility

The performance of mobile ad hoc networks in general and that of the routing algorithm, in particular, can be heavily affected by the intrinsic dynamic nature of the underlying topology. In this paper, we build a new analytical/numerical framework that characterizes nodes' mobility and the evolution of links between them. This formulation is based on a stationary Markov chain representation of link connectivity. The existence of a link between two nodes depends on their distance, which is governed by the mobility model. In our analysis, nodes move randomly according to an Ornstein-Uhlenbeck process using one tuning parameter to obtain different levels of randomness in the mobility pattern. Finally, we propose an entropy-rate-based metric that quantifies link uncertainty and evaluates its stability. Numerical results show that the proposed approach can accurately reflect the random mobility in the network and fully captures the link dynamics. It may thus be considered a valuable performance metric for the evaluation of the link stability and connectivity in these networks.Comment: 6 pages, 4 figures, Submitted to IEEE International Conference on Communications 201

SAnoVs: Secure Anonymous Voting Scheme for clustered ad hoc networks

In this paper we propose a secure anonymous voting scheme (SAnoVS) for re-clustering in the ad-hoc network. SAnoVS extends our previous work of degree-based clustering algorithms by achieving anonymity and confidentiality of the voting procedure applied to select new cluster heads. The security of SAnoVS is based on the difficulty of computing discrete logarithms over elliptic curves, the intractability of inverting a one-way hash function and the fact that only neighboring nodes contribute to the generation of a shared secret. Furthermore, we achieve anonymity since our scheme does not require any identification information as we make use of a polynomial equation system combined with pseudo-random coordinates. The security analysis of our scheme is demonstrated with several attacks scenarios.examined with several attack scenarios and experimental results

Shortest, Fastest, and Foremost Broadcast in Dynamic Networks

Highly dynamic networks rarely offer end-to-end connectivity at a given time. Yet, connectivity in these networks can be established over time and space, based on temporal analogues of multi-hop paths (also called {\em journeys}). Attempting to optimize the selection of the journeys in these networks naturally leads to the study of three cases: shortest (minimum hop), fastest (minimum duration), and foremost (earliest arrival) journeys. Efficient centralized algorithms exists to compute all cases, when the full knowledge of the network evolution is given. In this paper, we study the {\em distributed} counterparts of these problems, i.e. shortest, fastest, and foremost broadcast with termination detection (TDB), with minimal knowledge on the topology. We show that the feasibility of each of these problems requires distinct features on the evolution, through identifying three classes of dynamic graphs wherein the problems become gradually feasible: graphs in which the re-appearance of edges is {\em recurrent} (class R), {\em bounded-recurrent} (B), or {\em periodic} (P), together with specific knowledge that are respectively $n$ (the number of nodes), $\Delta$ (a bound on the recurrence time), and $p$ (the period). In these classes it is not required that all pairs of nodes get in contact -- only that the overall {\em footprint} of the graph is connected over time. Our results, together with the strict inclusion between $P$, $B$, and $R$, implies a feasibility order among the three variants of the problem, i.e. TDB[foremost] requires weaker assumptions on the topology dynamics than TDB[shortest], which itself requires less than TDB[fastest]. Reversely, these differences in feasibility imply that the computational powers of $R_n$, $B_\Delta$, and $P_p$ also form a strict hierarchy

Synchronization in Random Geometric Graphs

In this paper we study the synchronization properties of random geometric graphs. We show that the onset of synchronization takes place roughly at the same value of the order parameter that a random graph with the same size and average connectivity. However, the dependence of the order parameter with the coupling strength indicates that the fully synchronized state is more easily attained in random graphs. We next focus on the complete synchronized state and show that this state is less stable for random geometric graphs than for other kinds of complex networks. Finally, a rewiring mechanism is proposed as a way to improve the stability of the fully synchronized state as well as to lower the value of the coupling strength at which it is achieved. Our work has important implications for the synchronization of wireless networks, and should provide valuable insights for the development and deployment of more efficient and robust distributed synchronization protocols for these systems.Comment: 5 pages, 4 figure