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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Posted Content
A Practical Algorithm with Performance Guarantees for the Art~Gallery Problem
Simon Hengeveld,Tillmann Miltzow +1 more
TL;DR: A one-shot vision stable algorithm that computes an optimal guard set for visionstable polygons using polynomial time and solving one integer program guarantees to find the optimal solution for every vision stable polygon.
Journal ArticleDOI
Shortest Path Problems on a Polyhedral Surface
Atlas F. Cook,Carola Wenk +1 more
TL;DR: Agarwal et al. as mentioned in this paper describe algorithms to compute edge sequences, a shortest path map, and the Frechet distance for a convex polyhedral surface, where distances on the surface are measured by the length of a Euclidean shortest path.
Journal ArticleDOI
A nearly optimal algorithm for the geodesic voronoi diagram of points in a simple polygon
TL;DR: A construction algorithm is given that is nearly optimal in the sense that if a single Voronoi vertex can be computed in O ( log n ) time, then the construction time will become the optimal O ( n + m log m ) .
Book ChapterDOI
Incremental Algorithms to Update Visibility Polygons
R. Inkulu,Nitish P. Thakur +1 more
TL;DR: This work considers the problem of updating the visibility polygon of a point located within the given simple polygon as that polygon is modified with the incremental addition of new vertices to it and proposes the following two semi-dynamic algorithms.
Proceedings Article
Shortest Paths in the Plane with Obstacle Violations.
TL;DR: A tight bound of Θ(kn) on the size of this map is proved, and it is shown that it can be computed in O(k2n logn) time, where n is the total number of obstacle vertices.
References
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Book
Data Structures and Network Algorithms
TL;DR: This paper presents a meta-trees tree model that automates the very labor-intensive and therefore time-heavy and therefore expensive process of manually selecting trees to grow in a graph.
Journal ArticleDOI
Self-adjusting binary search trees
TL;DR: The splay tree, a self-adjusting form of binary search tree, is developed and analyzed and is found to be as efficient as balanced trees when total running time is the measure of interest.
Journal ArticleDOI
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.