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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TLDR
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
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Landmark selection strategies for path execution
TL;DR: This work presents several formulations of the problem of finding which k landmarks the robot should detect and track over which segments of a path, so that the cost of sensing (detection and tracking) is minimized, and presents a graph-theoretic approach to this problem.
Journal ArticleDOI
Approximability of guarding weak visibility polygons
TL;DR: For weak visibility polygons with holes, King and Kirkpatrick as discussed by the authors showed that there is no polynomial time algorithm with an approximation ratio better than ( 1 − ϵ )/12 ) ln n for any ϵ > 0 unless N P = P.
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Optimal Power Management with Guaranteed Minimum Energy Utilization for Solar Energy Harvesting Systems
TL;DR: The Stochastic Power Management (SPM) scheme, which builds statistical models of harvested energy based on historical data, maximizes the lowest energy consumption across all time intervals while giving strict probabilistic guarantees on not encountering battery depletion.
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Computing the Optimal Bridge between Two Polygons
Sung Kwon Kim,Chan-Su Shin +1 more
TL;DR: This work considers the problem of finding an optimal bridge between P and Q, such that the length of the longest path from a point in P, passing through the bridge (p,q) , to a point Q is minimized.
References
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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.