Computational geometry: an introduction
Computational geometry: an introduction
Approximation algorithms for shortest path motion planning
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Rectilinear shortest paths through polygonal obstacles in O(n(logn)2) time
SCG '87 Proceedings of the third annual symposium on Computational geometry
Information Processing Letters
Visibility and intersection problems in plane geometry
Discrete & Computational Geometry
Shortest watchman routes in simple polygons
Discrete & Computational Geometry
Shortest path queries in rectilinear worlds of higher dimension (extended abstract)
SCG '91 Proceedings of the seventh annual symposium on Computational geometry
Watchman routes under limited visibility
Computational Geometry: Theory and Applications
Information Sciences: an International Journal
Dynamic point location in general subdivisions
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A pedestrian approach to ray shooting: shoot a ray, take a walk
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Precision-sensitive Euclidean shortest path in 3-space (extended abstract)
Proceedings of the eleventh annual symposium on Computational geometry
Shortest zookeeper's routes in simple polygons
Information Processing Letters
Fast computation of shortest watchman routes in simple polygons
Information Processing Letters
Pseudo approximation algorithms, with applications to optimal motion planning
Proceedings of the eighteenth annual symposium on Computational geometry
An O(n log n) algorithm for the zoo-keeper's problem
Computational Geometry: Theory and Applications - Fourth CGC workshop on computional geometry
Shortest Safari Routes in Simple Polygon
ISAAC '94 Proceedings of the 5th International Symposium on Algorithms and Computation
New results on shortest paths in three dimensions
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Shortest paths in simple polygons with polygon-meet constraints
Information Processing Letters
Query-point visibility constrained shortest paths in simple polygons
Theoretical Computer Science
Efficiently determining a locally exact shortest path on polyhedral surfaces
Computer-Aided Design
Visiting a Polygon on the Optimal Way to a Query Point
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
On A☆ search with stopover areas
International Journal of Geographical Information Science
Computers and Electronics in Agriculture
Inspecting a Set of Strips Optimally
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
An efficient algorithm for relay placement in a ring sensor networks
Expert Systems with Applications: An International Journal
An approximate algorithm for solving the watchman route problem
RobVis'08 Proceedings of the 2nd international conference on Robot vision
An approximation algorithm for computing minimum-length polygons in 3D images
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part IV
Largest and smallest tours and convex hulls for imprecise points
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Linear-Time 2-approximation algorithm for the watchman route problem
TAMC'06 Proceedings of the Third international conference on Theory and Applications of Models of Computation
Visiting a sequence of points with a bevel-tip needle
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
Watchman tours for polygons with holes
Computational Geometry: Theory and Applications
Shortest paths in a cuboidal world
IWCIA'06 Proceedings of the 11th international conference on Combinatorial Image Analysis
Complexity of minimum corridor guarding problems
Information Processing Letters
Computing Geodesic Distances in Tree Space
SIAM Journal on Discrete Mathematics
Watchman routes for lines and segments
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
How Ants Can Efficiently Solve Generalized Watchman Route Problem
International Journal of Swarm Intelligence Research
Optimal patrolling of fragmented boundaries
Proceedings of the twenty-fifth annual ACM symposium on Parallelism in algorithms and architectures
Visiting convex regions in a polygonal map
Robotics and Autonomous Systems
Watchman routes for lines and line segments
Computational Geometry: Theory and Applications
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Given a sequence of k polygons in the plane, a start point s, and a target point, t, we seek a shortest path that starts at s, visits in order each of the polygons, and ends at t. If the polygons are disjoint and convex, we give an algorithm running in time O(kn log (n/k)), where n is the total number of vertices specifying the polygons. We also extend our results to a case in which the convex polygons are arbitrarily intersecting and the subpath between any two consecutive polygons is constrained to lie within a simply connected region; the algorithm uses O(nk2 log n) time. Our methods are simple and allow shortest path queries from s to a query point t to be answered in time O(k log n + m), where m is the combinatorial path length. We show that for nonconvex polygons this "touring polygons" problem is NP-hard.The touring polygons problem is a strict generalization of some classic problems in computational geometry, including the safari problem, the zoo-keeper problem, and the watchman route problem in a simple polygon. Our new results give an order of magnitude improvement in the running times of the safari problem and the watchman route problem: We solve the safari problem in O(n2 log n) time and the watchman route problem (through a fixed point s) in time O(n3 log n), compared with the previous time bounds of O(n3) and O(n4), respectively.