New data structures for orthogonal range queries
SIAM Journal on Computing
Adding range restriction capability to dynamic data structures
Journal of the ACM (JACM)
Computational geometry: an introduction
Computational geometry: an introduction
Halfplanar range search in linear space and O(n0.695) query time
Information Processing Letters
On the application of sheared retrieval to orthogonal range queries
SCG '86 Proceedings of the second annual symposium on Computational geometry
Filtering search: a new approach to query answering
SIAM Journal on Computing
Reduced memory space for multi-dimensional search trees
Proceedings on STACS 85 2nd annual symposium on theoretical aspects of computer science
A general approach to d-dimensional geometric queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Space-time tradeoffs for orthogonal range queries
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Efficient parallel solutions to some geometric problems
Journal of Parallel and Distributed Computing
Parallel processing for efficient subdivision search
SCG '87 Proceedings of the third annual symposium on Computational geometry
Optimal parallel algorithms for polygon and point-set problems
SCG '88 Proceedings of the fourth annual symposium on Computational geometry
A Lower Bound on the Complexity of Orthogonal Range Queries
Journal of the ACM (JACM)
Multidimensional divide-and-conquer
Communications of the ACM
Multidimensional binary search trees used for associative searching
Communications of the ACM
Design of Dynamic Data Structures
Design of Dynamic Data Structures
The Nearest Neighbor Problem on Bounded Domains
Proceedings of the 12th Colloquium on Automata, Languages and Programming
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Slimming down search structures: A functional approach to algorithm design
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Computing geographic nearest neighbors using monotone matrix searching (preliminary version)
CSC '90 Proceedings of the 1990 ACM annual conference on Cooperation
Ultra-fast expected time parallel algorithms
SODA '91 Proceedings of the second annual ACM-SIAM symposium on Discrete algorithms
Cache Oblivious Distribution Sweeping
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
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We define a new formalism called the quasi-valid range aggregation. This formalism leads to a new and quite simple method for reducing non-range query-like problems to range queries and often to orthogonal range queries, with immediate applications to the ATTRACTED NEIGHBOR and the planar ALL-PAIRS NEAREST NEIGHBORS problems (the latter being solved optimally on both parallel and sequential machines). A point of special interest is that our new formalism permits operators “+” that are neither associative nor abelian (unlike traditional range query theory). The technique described in this paper should therefore have significant other applications besides those we consider, especially in the context of parallel computational geometry.