Computational geometry: an introduction
Computational geometry: an introduction
On finding lowest common ancestors: simplification and parallelization (extended summary)
VLSI Algorithms and Architectures
SIAM Journal on Computing
Cascading divide-and-conquer: a technique for designing parallel algorithms
SIAM Journal on Computing
Optimal and sublogarithmic time randomized parallel sorting algorithms
SIAM Journal on Computing
Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
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
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
Parallel methods for visibility and shortest path problems in simple polygons (preliminary version)
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Randomized parallel algorithms for trapezoidal diagrams
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Ray shooting in polygons using Geodesic triangulations
Proceedings of the 18th international colloquium on Automata, languages and programming
A new data structure for shortest path queries in a simple polygon
Information Processing Letters
An optimal parallel algorithm for the visibility of a simple polygon from a point
Journal of the ACM (JACM)
Triangulating a simple polygon in linear time
Discrete & Computational Geometry
Fast Detection of Polyhedral Intersections
Proceedings of the 9th Colloquium on Automata, Languages and Programming
Dynamic ray shooting and shortest paths via balanced geodesic triangulations
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Static and kinetic geometric spanners with applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
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We provide optimal parallel solutions to several shortest path and visibility problems set in triangulated simple polygons. Let P be a triangulated simple polygon with n vertices, preprocessed to support shortest path queries. We can find the shortest path tree from any point inside P in O(log n) time using O(n/log n) processors. In the same bounds, we can preprocess P for shooting queries (a query can be answered in O(log n0 time by a uniprocessor). Given a set S of m points inside P, we can find an implicit representation of the relative convex hull of S in O(log(nm)) time with O(k/log(nm)) processors. All of these algorithms are deterministic and use the CREW PRAM model.