Preferential detachment in broadcast signaling networks: Connectivity and cost trade-off

We consider a network of nodes distributed in physical space without physical links communicating through message broadcasting over specified distances. Typically, communication using smaller distances is desirable due to savings in energy or other resources. We introduce a network formation mechanism to enable reducing the distances while retaining connectivity. Nodes, which initially transmit signals at a prespecified maximum distance, subject links to preferential detachment by autonomously decreasing their transmission radii while satisfying conditions of zero communication loss and fixed maximum node-hopping distance for signaling. Applied to networks with various spatial topologies, we find cost reductions as high as 90% over networks that are restricted to have all nodes with equal transmission distance. Copyright c © EPLA, 2007 Introduction. – The understanding of complex networks with physical links has been improving [1,2] yielding insights into network robustness to failure and attack [2–6], navigability [7], jamming and congestion [8–13], speed of information propagation [14], and efficient routing [15–19]. In this paper we study networks without physical links connected through virtual links created when a node sends out a broadcast signal by message carrier (e.g. radio wave, chemical) to all nearby nodes. Among a large number of such biological networks, neuronal molecular signaling (e.g. paracrine signaling) often involves the secretion of chemical signals onto a group of nearby target cells [20]. Broadcasting through electromagnetic transmission is used in multihop wireless networks, where messages may traverse multiple wireless links [21]. In both cases, localized broadcast transmission imposes key considerations. First, all nodes within the broadcast range of a transmitting node receive the signal, and only these nodes receive the signal (probabilistic distance-dependent links can occur [22]). Second, cyclical (a)On leave from the National Institute of Physics, University of the Philippines. retransmission of a signal is avoided using refractory periods or other methods. Third, there is a signal lifetime or a maximum number of retransmissions so as to discard stale information and prevent system overload. Fourth, to enable a node to respond to distinct signals from multiple other nodes smart protocols [23] use conflict avoidance, while many biological networks, including neural networks, use a large number of distinct chemicals for multiple channels [24,25], and radio networks often use labeled signal packets. Finally, such networks expend resources to transmit signals, with a cost that increases with the distance of transmission, a key consideration in the design of networks, whether chemical or radio. When barriers and other physical constraints effectively fix the spatial location of nodes and connectivity (whether direct or mediated) is required for all node pairs, the transmission distance of each node is the only variable of the system. Since the cost in energy or chemical messenger to establish links grows as a power of the transmission distance, D, where 2 α 4 for electromagnetic waves as well as chemical signals, the best cost reduction scheme will come from an effective reduction of the transmission distance. Truly autonomous wireless nodes