Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Making data structures persistent
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Trans-dichotomous algorithms for minimum spanning trees and shortest paths
Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Two- and three-dimensional point location in rectangular subdivisions
Journal of Algorithms
Efficient exact geometric computation made easy
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
A core library for robust numeric and geometric computation
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Journal of the ACM (JACM)
Integer Sorting in 0(n sqrt (log log n)) Expected Time and Linear Space
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator
FCRC '96/WACG '96 Selected papers from the Workshop on Applied Computational Geormetry, Towards Geometric Engineering
Two Simplified Algorithms for Maintaining Order in a List
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Dynamic Planar Convex Hull Operations in Near-Logarithmic Amortized Time
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Optimal External Memory Interval Management
SIAM Journal on Computing
Iterated snap rounding with bounded drift
Proceedings of the twenty-second annual symposium on Computational geometry
Planar Point Location in Sublogarithmic Time
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Voronoi diagrams in n · 2o(√lg lg n) time
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
A fast algorithm for three-dimensional layers of maxima problem
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Hi-index | 0.00 |
The dynamic convex hull problem was recently solved in O(lg n) time per operation, and this result is best possible in models of computation with bounded branching (e.g., algebraic computation trees). From a data structures point of view, however, such models are considered unrealistic because they hide intrinsic notions of information in the input.In the standard word-RAM and cell-probe models of computation, we prove that the optimal query time for dynamic convex hulls is, in fact, Theta(lg n / lglg n), for polylogarithmic update time (and word size). Our lower bound is based on a reduction from the marked-ancestor problem, and is one of the first data structural lower bounds for a nonorthogonal geometric problem. Our upper bounds follow a recent trend of attacking nonorthogonal geometric problems from an information-theoretic perspective that has proved central to advanced data structures. Interestingly, our upper bounds are the first to successfully apply this perspective to dynamic geometric data structures, and require substantially different ideas from previous work.