Journal ArticleDOI
Linear-time algorithms for visibility and shortest path problems inside triangulated simple polygons
Leonidas J. Guibas,John Hershberger,Daniel Leven,Micha Sharir,Micha Sharir,Robert E. Tarjan,Robert E. Tarjan +6 more
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Given a triangulation of a simple polygonP, linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP are presented.Abstract:
Given a triangulation of a simple polygonP, we present linear-time algorithms for solving a collection of problems concerning shortest paths and visibility withinP. These problems include calculation of the collection of all shortest paths insideP from a given source vertexS to all the other vertices ofP, calculation of the subpolygon ofP consisting of points that are visible from a given segment withinP, preprocessingP for fast "ray shooting" queries, and several related problems.read more
Citations
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Book ChapterDOI
Closest-Point Problems in Computational Geometry
TL;DR: Algorithms and data structures for proximity problems on point sets in ℝ D, including the closest pair problem, the exact and approximate post-office problem, and the problem of constructing spanners are discussed in detail.
Proceedings ArticleDOI
A pedestrian approach to ray shooting: shoot a ray, take a walk
John Hershberger,Subhash Suri +1 more
TL;DR: In this paper, a simple Steiner triangulation of a simple polygon with the property that a ray can intersect at most O(log n) triangles before reaching the polygon boundary is presented.
Journal ArticleDOI
Beyond intratransaction association analysis: mining multidimensional intertransaction association rules
Hongjun Lu,Ling Feng,Jiawei Han +2 more
TL;DR: The notion of multidimensional intertransaction association rules is introduced, their measurements and confidence are studied and their algorithms developed by extension of Apriori are overviewed, using the experience using the algorithms on both real-life and synthetic data sets.
Journal ArticleDOI
A survey of motion planning and related geometric algorithms
Proceedings ArticleDOI
Touring a sequence of polygons
TL;DR: The touring polygons problem is a strict generalization of some classic problems in computational geometry, including the safari problem, the zoo-keeper problem, and the watchman route problem in a simple polygon and it is shown that for nonconvex polygons this "touring polygons" problem is NP-hard.
References
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Book
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Self-adjusting binary search trees
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Optimal Search in Planar Subdivisions
TL;DR: This work presents a practical algorithm for subdivision search that achieves the same (optimal) worst case complexity bounds as the significantly more complex algorithm of Lipton and Tarjan, namely $O(\log n)$ search time with $O(n)$ storage.
Journal ArticleDOI
Optimal point location in a monotone subdivision
TL;DR: A substantial refinement of the technique of Lee and Preparata for locating a point in $\mathcal{S}$ based on separating chains is exhibited, which can be implemented in a simple and practical way, and is extensible to subdivisions with edges more general than straight-line segments.
Journal ArticleDOI
Euclidean shortest paths in the presence of rectilinear barriers
Der-Tsai Lee,Franco P. Preparata +1 more
TL;DR: The goal is to find interesting cases for which the solution can be obtained without the explicit construction of the entire visibility graph, which solve the problems by constructing the shortest-path tree from the source to all the vertices of the obstacles and to the destination.