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}
}
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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SHOWING 1-9 OF 9 REFERENCES

Graphics in flatland: A case study

  • H. Edelsbrunner, M. Overmars, D. Wood
  • in: F. Preparata, ed., Advances in Computing…
  • 1983
1 Excerpt

The power of geometric duality

  • B. Chazelle, L.J, Guibas, D. T. Lee
  • in: Prec. 24th Ann. IEEE Symp. on Foundations of…
  • 1983
2 Excerpts

Proximity and reachability in the plane

  • D. T. Lee
  • Ph.D. Thesis, University of Ilfinois at Urbana…
  • 1978

A note on two problems in connection with graphs

  • E. W. Dijkstra
  • Numer. Math. 1
  • 1959
1 Excerpt

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