An Output Sensitive Algorithm for Computing Visibility Graphs

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.

Authors

• Subir Kumar Ghosh
• David M. Mount

Keywords

• Computer science
• Computational geometry
• Computer applications
• Tree graphs
• Educational institutions
• Military computing
• Automation
• Sorting
• Fingers
• Clocks
• Shortest Path
• Line Segment
• Visibility Graph
• Pair Of Vertices
• N Log N
• Contralateral
• Running Time
• Time Constant
• Directed Graph
• Version Of The Paper
• Linear Order
• Lower Edge
• Natural Order
• Upper Edge
• Proof Of The Lemma
• Clockwise And Counterclockwise
• Depth-first
• P Forms
• Split Procedure
• Dijkstra’s Algorithm
• Tangent Point
• Polygon Boundaries
• Preorder