Lower Bounds for Shortest Path and Related ProblemsJohn
@inproceedings{Canny1987LowerBF, title={Lower Bounds for Shortest Path and Related ProblemsJohn}, author={J. Canny and J. Reif}, year={1987} }
We present the rst lower bounds for shortest path problems (including euclidean shortest path) in three dimensions, and for some constrained motion planning problems in two and three dimensions. Our proofs are based a technique called free path encoding and use homotopy equivalence classes of paths to encode state. We rst apply the method to the shortest path problem in three dimensions. The problem is to nd the shortest path under an L metric (e.g. a euclidean metric) between two points amid… CONTINUE READING
Figures from this paper
15 Citations
Nonpositive Curvature and Pareto Optimal Coordination of Robots
- Mathematics, Computer Science
- SIAM J. Control. Optim.
- 2006
- 36
- PDF
Computing Geodesic Distances in Tree Space
- Mathematics, Computer Science
- SIAM J. Discret. Math.
- 2011
- 40
- PDF
A Genetic Algorithm for Shortest Path Motion Problem in Three Dimensions
- Computer Science
- ICIC
- 2007
- 1
- PDF
Rapid Multi-Query Path Planning For A Vertical Take-Off and Landing Unmanned Aerial Vehicle
- Engineering, Computer Science
- J. Aerosp. Comput. Inf. Commun.
- 2011
- 16
Footstep planning for humanoid robots: discrete and continuous approaches
- Computer Science, Engineering
- 2011
- 3
- PDF
Computing Pareto Optimal Coordinations on Roadmaps
- Mathematics, Computer Science
- Int. J. Robotics Res.
- 2005
- 50
- Highly Influenced
- PDF
References
SHOWING 1-10 OF 19 REFERENCES
A new algebraic method for robot motion planning and real geometry
- Computer Science
- 28th Annual Symposium on Foundations of Computer Science (sfcs 1987)
- 1987
- 114
On the Complexity of Motion Planning for Multiple Independent Objects; PSPACE- Hardness of the "Warehouseman's Problem"
- Mathematics
- 1984
- 269
On the “piano movers” problem. II. General techniques for computing topological properties of real algebraic manifolds
- Mathematics
- 1983
- 894
- PDF
An algorithm for planning collision-free paths among polyhedral obstacles
- Computer Science
- CACM
- 1979
- 2,283
- PDF