Highly Influenced

# Constructing the Visibility Graph for n-Line Segments in O(n²) Time

@article{Welzl1985ConstructingTV, title={Constructing the Visibility Graph for n-Line Segments in O(n²) Time}, author={Emo Welzl}, journal={Inf. Process. Lett.}, year={1985}, volume={20}, pages={167-171} }

- Published in Inf. Process. Lett. 1985
DOI:10.1016/0020-0190(85)90044-4

Given a set S of line segments in the plane, its visibility graph G s is the undirected graph which has the endpoints of the line segments in S as nodes and in which two nodes (points) are adjacent whenever they 'see' each other (the line segments in S are regarded as nontransparent obstacles). It is shown that G s can be constructed in O(n 2) time and space for a set S of n nonintersecting line segments. As an immediate implication, the shortest path between two points in the plane avoiding a… CONTINUE READING

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