Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
Reporting points in halfspaces
Computational Geometry: Theory and Applications
Two- and three-dimensional point location in rectangular subdivisions
Journal of Algorithms
Efficient 3-D range searching in external memory
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Algorithms for three-dimensional dominance searching in linear space
Information Processing Letters
On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
The P-range tree: a new data structure for range searching in secondary memory
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Vertical Decomposition of Shallow Levels in 3-Dimensional Arrangements and Its Applications
SIAM Journal on Computing
Efficient searching with linear constraints
Journal of Computer and System Sciences - Special issue on the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on principles of database systems
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
New data structures for orthogonal range searching
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
On approximate halfspace range counting and relative epsilon-approximations
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
A data structure for multi-dimensional range reporting
SCG '07 Proceedings of the twenty-third annual symposium on Computational geometry
I/O-efficient point location in a set of rectangles
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Space Efficient Multi-dimensional Range Reporting
COCOON '09 Proceedings of the 15th Annual International Conference on Computing and Combinatorics
Data Structures for Approximate Orthogonal Range Counting
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Cell probe lower bounds and approximations for range mode
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Range-aggregate queries involving geometric aggregation operations
WALCOM'11 Proceedings of the 5th international conference on WALCOM: algorithms and computation
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
Three problems about dynamic convex hulls
Proceedings of the twenty-seventh annual symposium on Computational geometry
I/O-efficient data structures for colored range and prefix reporting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Persistent predecessor search and orthogonal point location on the word RAM
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Improved space bounds for cache-oblivious range reporting
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
External memory orthogonal range reporting with fast updates
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Higher-dimensional orthogonal range reporting and rectangle stabbing in the pointer machine model
Proceedings of the twenty-eighth annual symposium on Computational geometry
Persistent Predecessor Search and Orthogonal Point Location on the Word RAM
ACM Transactions on Algorithms (TALG) - Special Issue on SODA'11
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In this paper, we study the 3D dominance reporting problem in different models of computations and offer optimal results in the pointer machine and the external memory models and a near optimal result in the RAM model; all our results consume linear space. We can answer queries in O(log n+ k) time on a pointer machine, with O(logBn+ k/B) I/Os in the external memory model and in O((log logn)2+ log log U+ k) time in the RAM model and in a U×U×Uinteger grid. These improve the results of various papers, such as Makris and Tsakalidis (IPL'98), Vengroff and Vitter (STOC'96) and Nekrich (SOCG'07). Here, n, kand Bare the input, output and block size respectively. With a log3nfold increase in the space complexity these can be turned into orthogonal range reporting algorithms with matching query times, improving the previous orthogonal range searching results in the pointer machine and RAM models. Using our 3D results as base cases, we can provide improved orthogonal range reporting algorithms in 茂戮驴d, d茂戮驴 4. We use randomization only in the preprocessing part and our query bounds are all worst case.