The input/output complexity of sorting and related problems
Communications of the ACM
Reporting points in halfspaces
Computational Geometry: Theory and Applications
On the analysis of indexing schemes
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Algorithms for three-dimensional dominance searching in linear space
Information Processing Letters
On two-dimensional indexability and optimal range search indexing
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
On range reporting, ray shooting and k-level construction
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Exponential Structures for Efficient Cache-Oblivious Algorithms
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Cache-oblivious data structures for orthogonal range searching
Proceedings of the nineteenth annual symposium on Computational geometry
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Cache-oblivious planar orthogonal range searching and counting
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Simple and semi-dynamic structures for cache-oblivious planar orthogonal range searching
Proceedings of the twenty-second annual symposium on Computational geometry
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Optimal halfspace range reporting in three dimensions
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Cache-oblivious range reporting with optimal queries requires superlinear space
Proceedings of the twenty-fifth annual symposium on Computational geometry
A general approach for cache-oblivious range reporting and approximate range counting
Computational Geometry: Theory and Applications
Cache-Oblivious Range Reporting with Optimal Queries Requires Superlinear Space
Discrete & Computational Geometry - Special Issue: 25th Annual Symposium on Computational Geometry; Guest Editor: John Hershberger
I/O-efficient data structures for colored range and prefix reporting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We provide improved bounds on the size of cache-oblivious range reporting data structures that achieve the optimal query bound of O(logB N + K/B) block transfers. Our first main result is an O(N√log N log log N)-space data structure that achieves this query bound for 3-d dominance reporting and 2-d three-sided range reporting. No cache-oblivious o(N log N/log log N)-space data structure for these problems was known before, even when allowing a query bound of O(log2O(1) N + K/B) block transfers. Our result also implies improved space bounds for general 2-d and 3-d orthogonal range reporting. Our second main result shows that any cache-oblivious 2-d three-sided range reporting data structure with the optimal query bound has to use Ω(N logε N) space, thereby improving on a recent lower bound for the same problem. Using known transformations, the lower bound extends to 3-d dominance reporting and 3-d halfspace range reporting.