Filtering search: a new approach to query answering
SIAM Journal on Computing
Functional approach to data structures and its use in multidimensional searching
SIAM Journal on Computing
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
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
CRB-Tree: An Efficient Indexing Scheme for Range-Aggregate Queries
ICDT '03 Proceedings of the 9th International Conference on Database Theory
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
Simple and semi-dynamic structures for cache-oblivious planar orthogonal range searching
Proceedings of the twenty-second annual symposium on Computational geometry
Engineering a cache-oblivious sorting algorithm
Journal of Experimental Algorithmics (JEA)
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
Cache-oblivious index for approximate string matching
Theoretical Computer Science
I/O-efficient data structures for colored range and prefix reporting
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Ordered and unordered top-K range reporting in large data sets
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
Cache-oblivious index for approximate string matching
CPM'07 Proceedings of the 18th annual conference on Combinatorial Pattern Matching
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We present the first cache-oblivious data structure for planar orthogonal range counting, and improve on previous results for cache-oblivious planar orthogonal range searching.Our range counting structure uses O(N log2 N) space and answers queries using O(logB N) memory transfers, where B is the block size of any memory level in a multilevel memory hierarchy. Using bit manipulation techniques, the space can be further reduced to O(N). The structure can also be modified to support more general semigroup range sum queries in O(logB N) memory transfers, using O(N log2 N) space for three-sided queries and O(N log22 N/log2 log2 N) space for four-sided queries.Based on the O(N log N) space range counting structure, we develop a data structure that uses O(N log2 N) space and answers three-sided range queries in O(logB N+T/B) memory transfers, where T is the number of reported points. Based on this structure, we present a general four-sided range searching structure that uses O(N log22 N/log2 log2 N) space and answers queries in O(logB N + T/B) memory transfers.