On the continuous Weber and k-median problems (extended abstract)
Proceedings of the sixteenth annual symposium on Computational geometry
ACM SIGACT News
Computing shortest paths with comparisons and additions
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
A global optimal approach to facility location in the presence of forbidden regions
Computers and Industrial Engineering
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
Dynamic coverage in ad-hoc sensor networks
Mobile Networks and Applications
Curvature-bounded traversals of narrow corridors
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Fast exact and approximate geodesics on meshes
ACM SIGGRAPH 2005 Papers
The transportation metric and related problems
Information Processing Letters
An optimal-time algorithm for shortest paths on a convex polytope in three dimensions
Proceedings of the twenty-second annual symposium on Computational geometry
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
Boundary recognition in sensor networks by topological methods
Proceedings of the 12th annual international conference on Mobile computing and networking
Fast arbitrary splitting of deforming objects
Proceedings of the 2006 ACM SIGGRAPH/Eurographics symposium on Computer animation
Shortest paths on realistic polyhedra
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Querying approximate shortest paths in anisotropic regions
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Flying over a polyhedral terrain
Information Processing Letters
Approximate distance oracles for geometric spanners
ACM Transactions on Algorithms (TALG)
Walking your dog in the woods in polynomial time
Proceedings of the twenty-fourth annual symposium on Computational geometry
Parallel algorithms for approximation of distance maps on parametric surfaces
ACM Transactions on Graphics (TOG)
Shortest Path Queries in Polygonal Domains
AAIM '08 Proceedings of the 4th international conference on Algorithmic Aspects in Information and Management
Visiting a Polygon on the Optimal Way to a Query Point
FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
Feed-links for network extensions
Proceedings of the 16th ACM SIGSPATIAL international conference on Advances in geographic information systems
Approximate Euclidean shortest paths amid convex obstacles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Graph-Theoretic Concepts in Computer Science
Efficient Boustrophedon Multi-Robot Coverage: an algorithmic approach
Annals of Mathematics and Artificial Intelligence
The geodesic farthest-site Voronoi diagram in a polygonal domain with holes
Proceedings of the twenty-fifth annual symposium on Computational geometry
Planar rectilinear shortest path computation using corridors
Computational Geometry: Theory and Applications
Link Distance and Shortest Path Problems in the Plane
AAIM '09 Proceedings of the 5th International Conference on Algorithmic Aspects in Information and Management
Shortest Path Problems on a Polyhedral Surface
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Maximum thick paths in static and dynamic environments
Computational Geometry: Theory and Applications
Homotopic Fréchet distance between curves or, walking your dog in the woods in polynomial time
Computational Geometry: Theory and Applications
Computational Geometry: Theory and Applications - Special issue on the Japan conference on discrete and computational geometry 2004
Splitting meshless deforming objects with explicit surface tracking
Graphical Models
Querying Two Boundary Points for Shortest Paths in a Polygonal Domain
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
The transportation metric and related problems
Information Processing Letters
Approximation algorithms for shortest descending paths in terrains
Journal of Discrete Algorithms
Compact oracles for approximate distances around obstacles in the plane
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Finding a rectilinear shortest path in R2using corridor based staircase structures
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
PerPos: a platform providing cloud services for pervasive positioning
Proceedings of the 1st International Conference and Exhibition on Computing for Geospatial Research & Application
Geodesic Fréchet distance inside a simple polygon
ACM Transactions on Algorithms (TALG)
The geodesic diameter of polygonal domains
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Approximate solution of the multiple watchman routes problem with restricted visibility range
IEEE Transactions on Neural Networks
Shortest paths with arbitrary clearance from navigation meshes
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
Navigation queries from triangular meshes
MIG'10 Proceedings of the Third international conference on Motion in games
Querying Approximate Shortest Paths in Anisotropic Regions
SIAM Journal on Computing
Continuous nearest-neighbor search in the presence of obstacles
ACM Transactions on Database Systems (TODS)
Information and Computation
Computational Geometry: Theory and Applications
Link distance and shortest path problems in the plane
Computational Geometry: Theory and Applications
A nearly optimal algorithm for finding L1shortest paths among polygonal obstacles in the plane
ESA'11 Proceedings of the 19th European conference on Algorithms
Asynchronous deterministic rendezvous in bounded terrains
Theoretical Computer Science
Delineating imprecise regions via shortest-path graphs
Proceedings of the 19th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems
Shortest non-crossing walks in the plane
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Computing shortest paths amid pseudodisks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Semi-automated data center hotspot diagnosis
Proceedings of the 7th International Conference on Network and Services Management
Querying two boundary points for shortest paths in a polygonal domain
Computational Geometry: Theory and Applications
Asynchronous deterministic rendezvous in bounded terrains
SIROCCO'10 Proceedings of the 17th international conference on Structural Information and Communication Complexity
Farthest voronoi diagrams under travel time metrics
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Shortest path problem in rectangular complexes of global nonpositive curvature
Computational Geometry: Theory and Applications
Indoor pedestrian navigation based on hybrid route planning and location modeling
Pervasive'12 Proceedings of the 10th international conference on Pervasive Computing
A near-optimal algorithm for shortest paths among curved obstacles in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
Computing shortest paths among curved obstacles in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
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We propose an optimal-time algorithm for a classical problem in plane computational geometry: computing a shortest path between two points in the presence of polygonal obstacles. Our algorithm runs in worst-case time O(n log n) and requires O(n log n) space, where n is the total number of vertices in the obstacle polygons. The algorithm is based on an efficient implementation of wavefront propagation among polygonal obstacles, and it actually computes a planar map encoding shortest paths from a fixed source point to all other points of the plane; the map can be used to answer single-source shortest path queries in O(log n) time. The time complexity of our algorithm is a significant improvement over all previously published results on the shortest path problem. Finally, we also discuss extensions to more general shortest path problems, involving nonpoint and multiple sources.