WIP: Local Heuristics for Very Likely Connected and Intersection Free Wireless Network Topologies under Log-Normal Shadowing

Abstract

Local algorithms and other wireless network protocols require the underlying network graph to have specific structural properties to guarantee correctness. Two of these properties are connectivity and absence of intersecting links. Assuring only one of these properties is very often possible, either by considering a dense graph, which is very likely connected, but contains many intersections or a sparse graph which contains only few intersections, but is split up into many components. The task is therefore to choose the edges in a given graph in such a way that the intersections are removed while connectivity is preserved. Based on a Poisson point process and the log-normal shadowing model, we analyse the frequency of connected graphs without intersecting links. To further support such graph structure, we also restrict the maximal length of the edges in the network graph. By simulation we observe conditions how the maximal length of the edges in a graph should be chosen to assure the existence of a large component with few intersections.