Reachability Problems for Transmission Graphs

Let P be a set of n points in the plane where each point p is associated with radius \(r_p>0\). The transmission graph \(G=(P,E)\) defined as directed such that E contains an edge from to q if and only \(|pq|\le r_p\) for any two P, |pq| denotes Euclidean distance between q. In this paper, we present data structure size \(O(n^{5/3})\) can check \(O(n^{2/3})\) time there path G points. This first answering reachability queries whose performance depends on but not ratio largest smallest radii.