Reachability Problems for Transmission Graphs

06/09/2021

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by   Shinwoo An, et al.

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