Results 1 
3 of
3
SpaceEfficient and Fast Algorithms for Multidimensional Dominance Reporting and Counting
 PROCEEDINGS OF THE 15TH ISAAC, VOLUME 3341 OF LECTURE NOTES IN COMPUTER SCIENCE
, 2004
"... We present linearspace sublogarithmic algorithms for handling the 3dimensional dominance reporting and the 2dimensional dominance counting problems. Under the RAM model as described in [M. L. Fredman and D. E. Willard. “Surpassing the information theoretic bound with fusion trees”, Journal of C ..."
Abstract

Cited by 29 (1 self)
 Add to MetaCart
We present linearspace sublogarithmic algorithms for handling the 3dimensional dominance reporting and the 2dimensional dominance counting problems. Under the RAM model as described in [M. L. Fredman and D. E. Willard. “Surpassing the information theoretic bound with fusion trees”, Journal of Computer and System Sciences, 47:424– 436, 1993], our algorithms achieve O(log n / log log n + f) query time for the 3dimensional dominance reporting problem, where f is the output size, and O(log n / log log n) query time for the 2dimensional dominance counting problem. We extend these results to any constant dimension d ≥ 3, achieving O(n(log n / log log n) d−3) space and O((log n / log log n) d−2 + f) query time for the reporting case and O(n(log n / log log n) d−2) space and O((log n / log log n) d−1) query time for the counting case.
Uniquely Represented Data Structures for Computational Geometry
, 2008
"... We present new techniques for the construction of uniquely represented data structures in a RAM, and use them to construct efficient uniquely represented data structures for orthogonal range queries, line intersection tests, point location, and 2D dynamic convex hull. Uniquely represented data stru ..."
Abstract

Cited by 2 (2 self)
 Add to MetaCart
We present new techniques for the construction of uniquely represented data structures in a RAM, and use them to construct efficient uniquely represented data structures for orthogonal range queries, line intersection tests, point location, and 2D dynamic convex hull. Uniquely represented data structures represent each logical state with a unique machine state. Such data structures are strongly historyindependent. This eliminates the possibility of privacy violations caused by the leakage of information about the historical use of the data structure. Uniquely represented data structures may also simplify the debugging of complex parallel computations, by ensuring that two runs of a program that reach the same logical state reach the same physical state, even if various parallel processes executed in different orders during the two runs. 1
SpaceEfficient and Fast Algorithms for Multidimensional Dominance Reporting and Range Counting
"... We present linearspace sublogarithmic algorithms for handling the threedimensional dominance reporting problem and the twodimensional range counting problem. Under the RAM model as described in [M. L. Fredman and D. E. Willard. "Surpassing the information theoretic bound with fusion trees", Journ ..."
Abstract
 Add to MetaCart
We present linearspace sublogarithmic algorithms for handling the threedimensional dominance reporting problem and the twodimensional range counting problem. Under the RAM model as described in [M. L. Fredman and D. E. Willard. "Surpassing the information theoretic bound with fusion trees", Journal of Computer and System Sciences, 47:424436, 1993], our algorithms achieve O(log n = log log n + f) query time for 3D dominance reporting, where f is the number of points reported, and O(log n = log log n) query time for 2D range counting case. We extend these results to any constant dimension d achieving O(n(log n = log log n) d;3)space and O((log n = log log) d;2 + f)query time for the reporting case and O(n(log n = log log n) d;2)space and O((log n = log log n) d;1) query time for the counting case.