The input/output complexity of sorting and related problems
Communications of the ACM
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 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
Efficient splitting and merging algorithms for order decomposable problems
Information and Computation
Efficient cross-trees for external memory
External memory algorithms
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)
The K-D-B-tree: a search structure for large multidimensional dynamic indexes
SIGMOD '81 Proceedings of the 1981 ACM SIGMOD international conference on Management of data
Cache-oblivious data structures for orthogonal range searching
Proceedings of the nineteenth annual symposium on Computational geometry
On the limits of cache-obliviousness
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Random Sampling, Halfspace Range Reporting, and Construction of (= k)-Levels in Three Dimensions
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
The Cost of Cache-Oblivious Searching
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
The Priority R-tree: a practically efficient and worst-case optimal R-tree
SIGMOD '04 Proceedings of the 2004 ACM SIGMOD international conference on Management of data
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
Optimal halfspace range reporting in three dimensions
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
A general approach for cache-oblivious range reporting and approximate range counting
Proceedings of the twenty-fifth annual symposium on Computational geometry
A general approach for cache-oblivious range reporting and approximate range counting
Proceedings of the twenty-fifth annual symposium on Computational geometry
Introduction to the SIGACT news online algorithms column
ACM SIGACT News
On Developing New Models, with Paging as a Case Study
ACM SIGACT News
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A general approach for cache-oblivious range reporting and approximate range counting
Computational Geometry: Theory and Applications
I/O-efficient data structures for colored range and prefix reporting
Proceedings of the twenty-third 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
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We consider a number of range reporting problems in two and three dimensions and prove lower bounds on the amount of space required by any cache-oblivious data structure for these problems that achieves an optimal query bound of O(logBN + K/B) block transfers in the worst case, where K is the size of the query output. The problems we study are three-sided range reporting, 3-d dominance reporting, and 3-d halfspace range reporting. We prove that, in order to achieve the above query bound or even a bound of O((logB N)c (1 + K/B)), for any constant c 0, the structure has to use Ohmega(N (log log N)ε) space, where ε 0 is a constant that depends on c and on the constant hidden in the big-Oh notation of the query bound. Our result has a number of interesting consequences. The first one is a new type of separation between the I/O model and the cache-oblivious model, as I/O-efficient data structures with the optimal query bound and using linear or O(N logAST N) space are known for the above problems. The second consequence is the non-existence of a linear-space cache-oblivious persistent B-tree with worst-case optimal 1-d range reporting queries.