In a sensor network with information sources and a sink, we assume a single path between every location in the network and the destination. These abstract information paths represent the desired paths for transmission of information. If the number of sensor nodes is large enough to approximate information paths with a certain precision, we call the network implementable. In this paper, we investigate the relation between density of nodes and implementability of information paths. We show that a quadratic relation between the density of nodes and the magnitude of information flow does not guarantee implementability. On the other hand, we show that in a rectangular geometry with a line source and a line sink, and a total load of θ bps, N = O(θ2 log θ) number of nodes is sufficient for implementing the information paths. Furthermore, we show via simulation that adding the log factor is also a necessity for implementing the paths.
['Masoumeh Haghpanahi', 'Mehdi Kalantari', 'Mark A. Shayman']
Implementing Information Paths in a Dense Wireless Sensor Network