The input/output complexity of sorting and related problems
Communications of the ACM
Lower bounds for orthogonal range searching: I. The reporting case
Journal of the ACM (JACM)
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
ACM Computing Surveys (CSUR)
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
Cache-oblivious priority queue and graph algorithm applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Design of Dynamic Data Structures
Design of Dynamic Data Structures
A locality-preserving cache-oblivious dynamic dictionary
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Cache oblivious search trees via binary trees of small height
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
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
Exponential Structures for Efficient Cache-Oblivious Algorithms
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Cache Oblivious Distribution Sweeping
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Funnel Heap - A Cache Oblivious Priority Queue
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Scanning and Traversing: Maintaining Data for Traversals in a Memory Hierarchy
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Cache-oblivious data structures for orthogonal range searching
Proceedings of the nineteenth annual symposium on Computational geometry
External memory data structures
Handbook of massive data sets
On the limits of cache-obliviousness
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
FOCS '00 Proceedings of the 41st 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
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
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
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
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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In this paper, we develop improved cache-oblivious data structures for two- and three-sided planar orthogonal range searching. Our main result is an optimal static structure for two-sided range searching that uses linear space and supports queries in O(logBN + T/B) memory transfers, where B is the block size of any level in a multi-level memory hierarchy and T is the number of reported points. Our structure is the first linear-space cache-oblivious structure for a planar range searching problem with the optimal O(logBN + T/B) query bound. The structure is very simple, and we believe it to be of practical interest.We also show that our two-sided range search structure can be constructed cache-obliviously in O(N logBN) memory transfers. Using the logarithmic method and fractional cascading, this leads to a semi-dynamic linear-space structure that supports two-sided range queries in O(log2 N + T/B) memory transfers and insertions in O(log2N ⋅ logB N) memory transfers amortized. This structure is the first (semi-)dynamic structure for any planar range searching problem with a query bound that is logarithmic in the number of elements in the structure and linear in the output size.Finally, using a simple standard construction, we also obtain a static O(N log2 N)-space structure for three-sided range searching that supports queries in the optimal bound of O(logB N + T/B) memory transfers. These bounds match the bounds of the best previously known structure for this problem; but our structure is much simpler, simple enough, we believe, to be of practical interest.