An optimal parallel algorithm for detecting weak visibility of a simple polygon
TL;DR: This paper presents an optimal parallel algorithm for solving the problem of detecting the weak visibility of an n-vertex simple polygon P and shows that several other problems related to weak visibility can be optimally solved in parallel.
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Abstract: The problem of detecting the weak visibility of an n-vertex simple polygon P is that of finding whether P is weakly visible from one of its edges and (if it is) identifying every edge from which P is weakly visible. In this paper, we present an optimal parallel algorithm for solving this problem. Our algorithm runs in O(log n) time using O(n/log n) processors in the CREW PRAM computational model, and is very different from the sequential algorithms for this problem. Based on this algorithm, several other problems related to weak visibility can be optimally solved in parallel.
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Citations
Art Gallery and Illumination Problems
Jorge Urrutia
- 01 Jan 2000
TL;DR: Since Victor Klee's question, numerous variations on the art gallery problem have been studied, including mobile guards, guards with limited visibility or mobility, illumination of families of convex sets on the plane, guarding of rectilinear polygons, and others.
517
•Proceedings Article
LR-visibility in Polygons.
Gautam Das,Paul J. Heffernan,Giri Narasimhan +2 more
- 01 Jan 1993
TL;DR: A linear-time algorithm which, for a simple polygon P, computes all pairs of points s and t on P that admit LR-visibility, and says that P is LR-visible with respect to s andT if each point of P on the chain from s to t is visible from some point of the Chain from t to s.
50
Convex hull ranking algorithm for multi-objective evolutionary algorithms
TL;DR: This paper uses convex hull concepts to present a new ranking procedure for multi-objective evolutionary algorithms, and applies it as an alternative ranking procedure to NSGA-II for non-dominated comparisons, and test it using some benchmark problems.
22
Optimally Computing the Shortest Weakly Visible Subedge of a Simple Polygon
TL;DR: New geometric observations are presented that lead to extremely simple and optimal algorithms for solving the problem of computing the shortest weakly visible subedge of ann-vertex simple polygon, both sequentially and in parallel.
8
Determining Weak Visibility of a Polygon from an Edge in Parallel
TL;DR: This paper presents an optimal parallel algorithm for solving the problem of determining the weak visibility of an n-vertex simple polygon P from an edge e of P, and shows how to solve optimally, in parallel, several other problems that are related to theWeak visibility of simple polygons.
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References
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TL;DR: It is shown that one can exploit the ordering of the half-planes corresponding to the sequence of the polygon's edges to obtain a kernel finding algorithm which runs m time O(n) and is therefore optimal.
Computing the visibility polygon from an edge
Der-Tsai Lee,A. K. Lin +1 more
TL;DR: This work presents an O(n log n) algorithm for computing the visibility polygon, where n is the number of vertices of the polygon.
50
A linear-time algorithm for solving the strong hidden-line problem in a simple polygon
TL;DR: The algorithm combines results from visibility and shortest paths with the linear-time polygon triangulation algorithm discovered recently by Tarjan and Van Wyk to solve the strong hidden-line problem in a simple polygon P.
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Parallel methods for visibility and shortest path problems in simple polygons (preliminary version)
Michael T. Goodrich,Steven B. Shauck,Sumanta Guha +2 more
- 01 May 1990
TL;DR: Efficient parallel algorithms for solving a number of visibility and shortest path problems for simple polygons based on the use of a new data structure for implicitly representing all shortest paths in a simple polygon, which is called thestratified decomposition tree.
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