Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
An optimal algorithm for intersecting line segments in the plane
Journal of the ACM (JACM)
Applications of a new space-partitioning technique
Discrete & Computational Geometry
ACM Computing Surveys (CSUR)
A Unified Approach to Dynamic Point Location, Ray Shooting, and Shortest Paths in Planar Maps
SIAM Journal on Computing
Simplex range reporting on a pointer machine
Computational Geometry: Theory and Applications
An optimal real-time algorithm for planar convex hulls
Communications of the ACM
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Visibility Algorithms in the Plane
Visibility Algorithms in the Plane
Algorithms for Reporting and Counting Geometric Intersections
IEEE Transactions on Computers
Minimum-Perimeter Polygons of Digitized Silhouettes
IEEE Transactions on Computers
| Hi-index | 0.01 |
We present data structures for maintaining the relative convex hull of a set of points (sites) in the presence of pairwise non-crossing line segments (barriers) that subdivide a bounding box into simply connected faces. Our data structures have O((n+ m)logn) size for nsites and mbarriers. They support O(m) barrier insertions and O(n) site deletions in O((m+ n) polylog (mn)) total time, and can answer analogues of standard convex hull queries in O(polylog(mn)) time.Our data structures support a generalization of the sweep line technique, in which the sweep wavefrontmay have arbitrary polygonal shape, possibly bending around obstacles. We reduce the total time of monline updates of a polygonal sweep wavefront from $O(m\sqrt{n}\,{\rm polylog} n)$ to O((m+ n) polylog (mn)).