An output sensitive algorithm for computing visibility graphs

TitleAn output sensitive algorithm for computing visibility graphs
Publication TypeConference Papers
Year of Publication1987
AuthorsGhosh S K, Mount D
Conference NameFoundations of Computer Science, 1987., 28th Annual Symposium on
Date Published1987/10//

The visibility graph of a set of nonintersecting polygonal obstacles in the plane is an undirected graph whose vertices are the vertices of the obstacles and whose edges are pairs of vertices (u, v) such that the open line segment between u and v does not intersect any of the obstacles. The visibility graph is an important combinatorial structure in computational geometry and is used in applications such as solving visibility problems and computing shortest paths. An algorithm is presented that computes the visibility graph of s set of obstacles in time O(E + n log n), where E is the number of edges in the visibility graph and n is the total number of vertices in all the obstacles.