An important problem in wireless sensor networks is to find a minimal number of randomly deployed sensors making a network connected with a given probability. In practice sensors are often deployed one by one along a trajectory of a vehicle, so it is natural to assume that arbitrary probability density functions of distances between successive sensors are given.
A random distribution of sensors can be especially useful for monitoring long riversides and boundaries of restricted areas that are difficult of access. The paper computes the probability of connectivity of 1-dimensional networks and gives explicit estimates for a minimal number of sensors for important distributions. The paper is available in the arXiv (arXiv:0710.1001) and at http://maths.dur.ac.uk/~dma0vk/Research/connect.pdf.