A near-optimal algorithm for shortest paths among curved obstacles in the plane

Authors:
John Hershberger;Subhash Suri;Hakan Yıldız
Affiliations:
Mentor Graphics Corporation, Wilsonville, OR, USA;University of California, Santa Barbara, Santa Barbara, CA, USA;University of California, Santa Barbara, Santa Barbara, CA, USA
Venue:
Proceedings of the twenty-ninth annual symposium on Computational geometry
Year:
2013

Citing 18
Cited 2

Planar point location using persistent search trees

Communications of the ACM
On shortest paths in polyhedral spaces

SIAM Journal on Computing
On shortest paths amidst convex polyhedra

SIAM Journal on Computing
The discrete geodesic problem

SIAM Journal on Computing
An O(n2) shortest path algorithm for a non-rotating convex body

Journal of Algorithms
Efficient algorithms for Euclidean shortest path and visibility problems with polygonal obstacles

SCG '88 Proceedings of the fourth annual symposium on Computational geometry
An output-sensitive algorithm for computing visibility

SIAM Journal on Computing
Shortest paths among obstacles in the plane

SCG '93 Proceedings of the ninth annual symposium on Computational geometry
Shortest paths in the plane with polygonal obstacles

Journal of the ACM (JACM)
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
Shortest paths and networks

Handbook of discrete and computational geometry
Planning the shortest path for a disc in O(n2log n) time

SCG '85 Proceedings of the first annual symposium on Computational geometry
An Optimal Algorithm for Euclidean Shortest Paths in the Plane

SIAM Journal on Computing
An algorithm for planning collision-free paths among polyhedral obstacles

Communications of the ACM
Computing Point/Curve and Curve/Curve Bisectors

Proceedings of the 5th IMA Conference on the Mathematics of Surfaces
Approximate Euclidean shortest paths amid convex obstacles

SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Computing shortest paths amid pseudodisks

Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Computing 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
Technical note: On computing the shortest path in a multiply-connected domain having curved boundaries

Computer-Aided Design

Quantified Score

Hi-index	0.00

Visualization

Abstract

We propose an algorithm for the problem of computing shortest paths among curved obstacles in the plane. If the obstacles have O(n) description complexity, then the algorithm runs in O(n log n) time plus a term dependent on the properties of the boundary arcs. Specifically, if the arcs allow a certain kind of bisector intersection to be computed in constant time, or even in O(log n) time, then the running time of the overall algorithm is O(n log n). If the arcs support only constant-time tangent, intersection, and length queries, as is customarily assumed, then the algorithm computes an approximate shortest path, with relative error ε, in time O(n log n + n log 1/ε). In fact, the algorithm computes an approximate shortest path map, a data structure with O(n log n) size, that allows it to report the (approximate) length of a shortest path from a fixed source point to any query point in the plane in O(log n) time.