A fast algorithm for three-dimensional layers of maxima problem

Authors:
Yakov Nekrich
Affiliations:
Department of Computer Science, University of Bonn
Venue:
WADS'11 Proceedings of the 12th international conference on Algorithms and data structures
Year:
2011

Citing 23
Cited 0

Efficient data structures for range searching on a grid

Journal of Algorithms
A density control algorithm for doing insertions and deletions in a sequentially ordered file in a good worst-case time

Information and Computation
Dynamic maintenance of maximas of 2-d point sets

SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Biased finger trees and three-dimensional layers of maxima: (preliminary version)

SCG '94 Proceedings of the tenth annual symposium on Computational geometry
Two- and three-dimensional point location in rectangular subdivisions

Journal of Algorithms
Fast linear expected-time alogorithms for computing maxima and convex hulls

SODA '90 Proceedings of the first annual ACM-SIAM symposium on Discrete algorithms
On Finding the Maxima of a Set of Vectors

Journal of the ACM (JACM)
Output-size sensitive algorithms for finding maximal vectors

SCG '85 Proceedings of the first annual symposium on Computational geometry
A Sparse Table Implementation of Priority Queues

Proceedings of the 8th Colloquium on Automata, Languages and Programming
Cache Oblivious Distribution Sweeping

ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Two Simplified Algorithms for Maintaining Order in a List

ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Marked Ancestor Problems

FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Scaling and related techniques for geometry problems

STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Deterministic sorting in O(nlog logn) time and linear space

Journal of Algorithms
Three-Dimensional Layers of Maxima

Algorithmica
Planar Point Location in Sublogarithmic Time

FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Point Location in o(log n) Time, Voronoi Diagrams in o(n log n) Time, and Other Transdichotomous Results in Computational Geometry

FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Dynamic ordered sets with exponential search trees

Journal of the ACM (JACM)
Tight bounds for dynamic convex hull queries (again)

SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
Voronoi diagrams in n · 2o(√lg lg n) time

Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
More output-sensitive geometric algorithms

SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions

ACM Transactions on Algorithms (TALG)
Orthogonal range searching on the RAM, revisited

Proceedings of the twenty-seventh annual symposium on Computational geometry

Quantified Score

Hi-index	0.00

Visualization

Abstract

We show that the three-dimensional layers-of-maxima problem can be solved in o(n log n) time in the word RAM model. Our algorithm runs in O(n(log log n)3) deterministic time or O(n(log log n)2) expected time and uses O(n) space. We also describe a deterministic algorithm that uses optimal O(n) space and solves the three-dimensional layers-of-maxima problem in O(n log n) time in the pointer machine model.