Data structures and network algorithms
Data structures and network algorithms
A linear time algorithm with minimum link paths inside a simple polygon
Computer Vision, Graphics, and Image Processing
Visibility and intersectin problems in plane geometry
SCG '85 Proceedings of the first annual symposium on Computational geometry
Triangulating Simple Polygons and Equivalent Problems
ACM Transactions on Graphics (TOG)
Mathematics for the Analysis of Algorithms
Mathematics for the Analysis of Algorithms
A new representation for linear lists
STOC '77 Proceedings of the ninth annual ACM symposium on Theory of computing
Worst-case optimal algorithms for constructing visibility polygons with holes
SCG '86 Proceedings of the second annual symposium on Computational geometry
A linear-time algorithm for triangulating simple polygons
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Finding the visibility graph of a simple polygon in time proportional to its size
SCG '87 Proceedings of the third annual symposium on Computational geometry
Optimal shortest path queries in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
The all-geodesic furthest neighbor problem for simple polygons
SCG '87 Proceedings of the third annual symposium on Computational geometry
Joint triangulations and triangulation maps
SCG '87 Proceedings of the third annual symposium on Computational geometry
The furthest-site geodesic Voronoi diagram
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
An efficient algorithm for link-distance problems
SCG '89 Proceedings of the fifth annual symposium on Computational geometry
Parallel methods for visibility and shortest path problems in simple polygons (preliminary version)
SCG '90 Proceedings of the sixth annual symposium on Computational geometry
Dynamic trees and dynamic point location
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Planar separators and parallel polygon triangulation (preliminary version)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Dynamic ray shooting and shortest paths via balanced geodesic triangulations
SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Shortest paths in the plane with polygonal obstacles
Journal of the ACM (JACM)
An optimal algorithm for approximate nearest neighbor searching
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Efficient transmission of stored video for improved management of network bandwidth
International Journal of Network Management
Repairing Flaws in a Picture Based on a Geometric Representation of a Digital Image
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
Efficient visibility queries in simple polygons
Computational Geometry: Theory and Applications
Efficient computation of query point visibility in polygons with holes
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Dynamic and efficient key management for access hierarchies
Proceedings of the 12th ACM conference on Computer and communications security
Computing the Fréchet distance between simple polygons in polynomial time
Proceedings of the twenty-second annual symposium on Computational geometry
Thick non-crossing paths and minimum-cost flows in polygonal domains
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Query point visibility computation in polygons with holes
Computational Geometry: Theory and Applications
Efficiently determining a locally exact shortest path on polyhedral surfaces
Computer-Aided Design
An output sensitive algorithm for computing visibility graphs
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Processing an Offline Insertion-Query Sequence with Applications
FAW '09 Proceedings of the 3d International Workshop on Frontiers in Algorithmics
On the Complexity of Finding Paths in a Two-Dimensional Domain II: Piecewise Straight-Line Paths
Electronic Notes in Theoretical Computer Science (ENTCS)
Geodesic Fréchet distance inside a simple polygon
ACM Transactions on Algorithms (TALG)
Point location in the continuous-time moving network
AAIM'10 Proceedings of the 6th international conference on Algorithmic aspects in information and management
Hide-and-seek: algorithms for polygonWalk problems
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Continuous-time moving network voronoi diagram
Transactions on Computational Science XIV
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We present linear time algorithms for solving the following problems involving a simple planar polygon P: (i) Computing the collection of all shortest paths inside P from a given source vertex s to all the other vertices of P; (ii) Computing the subpolygon of P consisting of points that are visible from a segment within P; (iii) Preprocessing P so that for any query ray r emerging from some fixed edge e of P, we can find in logarithmic time the first intersection of r with the boundary of P; (iv) Preprocessing P so that for any query point x in P, we can find in logarithmic time the portion of the edge e that is visible from x; (v) Preprocessing P so that for any query point x inside P and direction u, we can find in logarithmic time the first point on the boundary of P hit by the ray at direction u from x; (vi) Calculating a hierarchical decomposition of P into smaller polygons by recursive polygon cutting, as in [Ch]. (vii) Calculating the (clockwise and counterclockwise) “convex ropes” (in the terminology of [PS]) from a fixed vertex s of P lying on its convex hull, to all other vertices of P. All these algorithms are based on a recent linear time algorithm of Tarjan and Van Wyk for triangulating a simple polygon, but use additional techniques to make all subsequent phases of these algorithms also linear.