Visibility of disjoint polygons
Algorithmica
Shortest paths in the plane with convex polygonal obstacles
Information Processing Letters
On the union of Jordan regions and collision-free translational motion amidst polygonal obstacles
Discrete & Computational Geometry
On shortest paths in polyhedral spaces
SIAM Journal on Computing
An O(n2) shortest path algorithm for a non-rotating convex body
Journal of Algorithms
New methods for computing visibility graphs
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
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 in the plane with polygonal obstacles
Journal of the ACM (JACM)
Computing the visibility graph via pseudo-triangulations
Proceedings of the eleventh annual symposium on 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
Computing the arrangement of curve segments: divide-and-conquer algorithms via sampling
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Shortest path amidst disc obstacles is computable
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Shortest path in a multiply-connected domain having curved boundaries
Computer-Aided Design
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
| Hi-index | 0.00 |
Multiple objects in the plane are called pseudodisks if they are convex and the boundaries of any two of them intersect transversely at most twice. Given a set of n (possibly intersecting) pseudodisks of O(1) complexity each and two points s and t in the plane, we develop an O(n2) time algorithm for computing a shortest s-to-t path avoiding the pseudodisks. In over two decades, the previously best algorithms for this problem take O(n2 log n) time, even when all pseudodisks are pairwise-disjoint disks. Our technique is also applicable to a motion planning problem of finding a shortest path to translate a convex object in the plane from one location to another avoiding a given set of polygonal obstacles, improving the previously best known solution. Our algorithm actually solves a more general version of the motion planning problem. Further, as a by-product of our approach, we present an O(n2) time algorithm for computing the visibility graph of a set of n (possibly intersecting) pseudodisks in the plane. The previously best known time bound of this visibility problem is O(n2 log n). In addition, for n pairwise disjoint (non-polygonal) convex objects of O(1) complexity each in the plane, we compute a shortest s-to-t path avoiding all objects in O(n log n + k) time, where k is the size of the visibility graph of the objects.