Abstract
Given n orthogonal line segments on the plane, their intersection graph is defined such that each vertex corresponds to a segment, and each edge corresponds to a pair of intersecting segments. Although this graph can have Θ(n 2) edges, we show that breadth first search can be accomplished in O(nlogn) time and O(n) space. As an application, we show that the minimum link rectilinear path between two points s and t amidst rectilinear polygonal obstacles can be computed in O(nlogn) time and O(n) space, which is optimal. We mention other related results in the paper.
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6 References
de Berg, On Rectilinear Link Distance, Computational Geometry: Theory and Application, to appear.
Clarkson, Kapoor, and Vaidya, Rectilinear Shortest Paths through Polygonal Obstacles in O(nlog2 n) time, ACM Symposium on Comp. Geometry, 1987.
Djidjev, Lingas, and Sack, An O(nlogn) Algorithm for Finding a Link Center in a Simple Polygon, Proceedings of Sixth STACS, Lecture Notes in Computer Science, Springer Verlag Series, 1989.
Edelsbrunner, Guibas, and Sharir, The Complexity of Many Faces in Arrangements of Lines and Segments, ACM Symposium on Comp. Geometry, 1988.
Fournier, and Montuno, Triangulating a Simple Polygon and Equivalent Problems, ACM Trans. on Graphics, 1984.
Ghosh, and Mount, An Output Sensitive Algorithm for Computing Visibility Graphs, IEEE FOCS, 1987.
Imai, and Asano, Efficient Algorithm for Geometric Graph Search Problems, SIAM J. of Comp., 1986.
Imai, and Asano, Dynamic Orthogonal Segment Intersection Search, J. of Algorithms, 8 (1987), pp. 1–18.
Ke, An Efficient Algorithm for Link Distance Problems, ACM Symposium on Comp. Geometry, 1989.
Krikpatrick, Optimal Search in Planar Subdivision, SIAM J. of Computing, 1983.
Lenhart, Pollack, Sack, Seidel, Sharir, Suri, Toussaint, Whitesides, and Yap, Computing the Link Center of a Simple Polygon, ACM Symposium on Comp. Geometry, 1987.
Mitchell, Rote, and Woeginger, Minimum Link Paths among Obstacles in the Plane, ACM Symposium on Comp. Geometry, 1990.
de Rezende, Lee, and Wu, Rectilinear Shortest Path with Rectangular Barriers, Discrete and Comp. Geometry, 1987.
Suri, A Linear Time Algorithm for Minimum Link Paths inside a Simple Polygon, Computer Vision, Graphics, Image Processing, 1986.
Suri, On some Link Distance Problems in a Simple Polygon, IEEE Trans. on Robotics and Automation, 1990.
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© 1991 Springer-Verlag Berlin Heidelberg
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Das, G., Narasimhan, G. (1991). Geometric searching and link distance. In: Dehne, F., Sack, JR., Santoro, N. (eds) Algorithms and Data Structures. WADS 1991. Lecture Notes in Computer Science, vol 519. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028268
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DOI: https://doi.org/10.1007/BFb0028268
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