Computational geometry: an introduction
Computational geometry: an introduction
Linear time algorithms for visibility and shortest path problems inside simple polygons
SCG '86 Proceedings of the second annual symposium on Computational geometry
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
SCG '87 Proceedings of the third annual symposium on Computational geometry
Adaptive bitonic sorting: an optimal parallel algorithm for shared-memory machines
SIAM Journal on Computing
Triangulating a polygon in parallel
Journal of Algorithms
Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
Optimal shortest path queries in a simple polygon
Journal of Computer and System Sciences
Computing geodesic furthest neighbors in simple polygons
Journal of Computer and System Sciences
Intersecting line segments in parallel with an output-sensitive number of processors
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Optimal parallel algorithms for transitive closure and point location in planar structures
SPAA '89 Proceedings of the first annual ACM symposium on Parallel algorithms and architectures
Optimal parallel algorithm for visibility of a simple polygon from a point
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Journal of the ACM (JACM)
Deterministic Parallel List Ranking
AWOC '88 Proceedings of the 3rd Aegean Workshop on Computing: VLSI Algorithms and Architectures
Intersecting is easier than sorting
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Constructing arrangements optimally in parallel (preliminary version)
SPAA '91 Proceedings of the third annual ACM symposium on Parallel algorithms and architectures
Planar separators and parallel polygon triangulation (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Gross motion planning—a survey
ACM Computing Surveys (CSUR)
Optimal parallel algorithms for triangulated simple polygons
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
An optimal parallel algorithm for detecting weak visibility of a simple polygon
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
High-Speed Environment Representation Scheme for Dynamic Path Planning
Journal of Intelligent and Robotic Systems
Environment Modelling for Robot Navigation Using VLSI-Efficient Logarithmic Approximation Method
Journal of Intelligent and Robotic Systems
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In this paper we give efficient parallel algorithms for solving a number of visibility and shortest path problems for simple polygons. Our algorithms all run in &Ogr;(log n) time and are based on the use of a new data structure for implicitly representing all shortest paths in a simple polygon P, which we call the stratified decomposition tree. We use this approach to derive efficient parallel methods for computing the visibility of P from an edge, constructing the visibility graph of the vertices of P (using an output-sensitive number of processors), constructing the shortest path tree from a vertex of P, and determining all-farthest neighbors for the vertices in P. The computational model we use is the CREW PRAM.