Davenport-Schinzel sequences and their geometric applications
Davenport-Schinzel sequences and their geometric applications
Kinetic data structures: a state of the art report
WAFR '98 Proceedings of the third workshop on the algorithmic foundations of robotics on Robotics : the algorithmic perspective: the algorithmic perspective
Data structures for mobile data
Journal of Algorithms
Kinetic binary space partitions for intersecting segments and disjoint triangles
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Cylindrical static and kinetic binary space partitions
Computational Geometry: Theory and Applications
Simplified kinetic connectivity for rectangles and hypercubes
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Static and kinetic geometric spanners with applications
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Separation Sensitive Kinetic Separation Structures for Convex Polygons
JCDCG '00 Revised Papers from the Japanese Conference on Discrete and Computational Geometry
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Kinetic collision detection between two simple polygons
Computational Geometry: Theory and Applications
Kinetic collision detection with fast flight plan changes
Information Processing Letters
Kinetic and dynamic data structures for closest pair and all nearest neighbors
ACM Transactions on Algorithms (TALG)
A kinetic triangulation scheme for moving points in the plane
Proceedings of the twenty-sixth annual symposium on Computational geometry
A kinetic triangulation scheme for moving points in the plane
Computational Geometry: Theory and Applications
Kinetic Euclidean minimum spanning tree in the plane
Journal of Discrete Algorithms
Kinetic pie delaunay graph and its applications
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Kinetic data structures for all nearest neighbors and closest pair in the plane
Proceedings of the twenty-ninth annual symposium on Computational geometry
| Hi-index | 0.00 |
Let S be a set of n moving points in the plane. We present a kinetic and dynamic (randomized) data structure for maintaining the convex hull of S. The structure uses O(n) space, and processes an expected number of O(n^2@b"s"+"2(n)logn) critical events, each in O(log^2n) expected time, including O(n) insertions, deletions, and changes in the flight plans of the points. Here s is the maximum number of times where any specific triple of points can become collinear, @b"s(q)=@l"s(q)/q, and @l"s(q) is the maximum length of Davenport-Schinzel sequences of order s on n symbols. Compared with the previous solution of Basch, Guibas and Hershberger [J. Basch, L.J. Guibas, J. Hershberger, Data structures for mobile data, J. Algorithms 31 (1999) 1-28], our structure uses simpler certificates, uses roughly the same resources, and is also dynamic.