2017/04/21 by Alexander P. Kartun-Giles, Sunwoo Kim, Kartun-Giles, Alexander P. +1 · 1 citation
Computer Science · #Cooperative Communication and Network Coding #FOS: Mathematics #Mobile Ad Hoc Networks #Opportunistic and Delay-Tolerant Networks #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1704.06400
openalex publication_date 2017/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study, via combinatorial enumeration, the probability of k-hop connection between two nodes in a wireless multi-hop network. This addresses the difficulty of providing an exact formula for the scaling of hop counts with Euclidean distance without first making a sort of mean field approximation, which in this case assumes all nodes in the network have uncorrelated degrees. We therefore study the mean and variance of the number of k-hop paths between two vertices x,y in the random connection model, which is a random geometric graph where nodes connect probabilistically rather than deterministically according to a critical connection range. In the example case where Rayleigh fading is modelled, the variance of the number of three hop paths is in fact composed of four separate decaying exponentials, one of which is the mean, which decays slowest as the Euclidean distance between the endpoints goes to infinity. These terms each correspond to one of exactly four distinct sub-structures with can form when pairs of paths intersect in a specific way, for example at exactly one node. Using a sum of factorial moments, this relates to the path existence probability. We also discuss a potential application of our results in bounding the broadcast time.