Investigating the Cost of Anonymity on Dynamic Networks

In this paper we study the difficulty of counting nodes in a synchronous dynamic network where nodes share the same identifier, they communicate by using a broadcast with unlimited bandwidth and, at each synchronous round, network topology may change. To count in such setting, it has been shown that the presence of a leader is necessary. We focus on a particularly interesting subset of dynamic networks, namely \textit{Persistent Distance} - ${\cal G}($PD$)_{h}$, in which each node has a fixed distance from the leader across rounds and such distance is at most $h$. In these networks the dynamic diameter $D$ is at most $2h$. We prove the number of rounds for counting in ${\cal G}($PD$)_{2}$ is at least logarithmic with respect to the network size $|V|$. Thanks to this result, we show that counting on any dynamic anonymous network with $D$ constant w.r.t. $|V|$ takes at least $D+ \Omega(\text{log}\, |V| )$ rounds where $\Omega(\text{log}\, |V|)$ represents the additional cost to be payed for handling anonymity. At the best of our knowledge this is the fist non trivial, i.e. different from $\Omega(D)$, lower bounds on counting in anonymous interval connected networks with broadcast and unlimited bandwith

Message and time efficient multi-broadcast schemes

We consider message and time efficient broadcasting and multi-broadcasting in wireless ad-hoc networks, where a subset of nodes, each with a unique rumor, wish to broadcast their rumors to all destinations while minimizing the total number of transmissions and total time until all rumors arrive to their destination. Under centralized settings, we introduce a novel approximation algorithm that provides almost optimal results with respect to the number of transmissions and total time, separately. Later on, we show how to efficiently implement this algorithm under distributed settings, where the nodes have only local information about their surroundings. In addition, we show multiple approximation techniques based on the network collision detection capabilities and explain how to calibrate the algorithms' parameters to produce optimal results for time and messages.Comment: In Proceedings FOMC 2013, arXiv:1310.459

Performance Limits and Geometric Properties of Array Localization

Location-aware networks are of great importance and interest in both civil and military applications. This paper determines the localization accuracy of an agent, which is equipped with an antenna array and localizes itself using wireless measurements with anchor nodes, in a far-field environment. In view of the Cram\'er-Rao bound, we first derive the localization information for static scenarios and demonstrate that such information is a weighed sum of Fisher information matrices from each anchor-antenna measurement pair. Each matrix can be further decomposed into two parts: a distance part with intensity proportional to the squared baseband effective bandwidth of the transmitted signal and a direction part with intensity associated with the normalized anchor-antenna visual angle. Moreover, in dynamic scenarios, we show that the Doppler shift contributes additional direction information, with intensity determined by the agent velocity and the root mean squared time duration of the transmitted signal. In addition, two measures are proposed to evaluate the localization performance of wireless networks with different anchor-agent and array-antenna geometries, and both formulae and simulations are provided for typical anchor deployments and antenna arrays.Comment: to appear in IEEE Transactions on Information Theor