Filtering search: a new approach to query answering
SIAM Journal on Computing
The input/output complexity of sorting and related problems
Communications of the ACM
The R*-tree: an efficient and robust access method for points and rectangles
SIGMOD '90 Proceedings of the 1990 ACM SIGMOD international conference on Management of data
On the analysis of indexing schemes
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A lower bound theorem for indexing schemes and its application to multidimensional range queries
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Tight bounds for 2-dimensional indexing schemes
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
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
The P-range tree: a new data structure for range searching in secondary memory
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Efficient splitting and merging algorithms for order decomposable problems
Information and Computation
Multidimensional binary search trees used for associative searching
Communications of the ACM
On a model of indexability and its bounds for range queries
Journal of the ACM (JACM)
Design of Dynamic Data Structures
Design of Dynamic Data Structures
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
R-trees: a dynamic index structure for spatial searching
SIGMOD '84 Proceedings of the 1984 ACM SIGMOD international conference on Management of data
Optimal Dynamic Range Searching in Non-replicating Index Structures
ICDT '99 Proceedings of the 7th International Conference on Database Theory
Optimal External Memory Interval Management
SIAM Journal on Computing
The limits of buffering: a tight lower bound for dynamic membership in the external memory model
Proceedings of the forty-second ACM symposium on Theory of computing
Approximate Range Searching in External Memory
Algorithmica
Using hashing to solve the dictionary problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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In the 2D orthogonal range search problem, we want to preprocess a set of 2D points so that, given any axis-parallel query rectangle, we can report all the data points in the rectangle efficiently. This paper presents a lower bound on the query time that can be achieved by any external memory structure that stores a point at most r times, where r is a constant integer. Previous research has resolved the bound at two extremes: r = 1, and r being arbitrarily large. We, on the other hand, derive the explicit tradeoff at every specific r. A premise that lingers in existing studies is the so-called indivisibility assumption: all the information bits of a point are treated as an atom, i.e., they are always stored together in the same block. We partially remove this assumption by allowing a data structure to freely divide a point into individual bits stored in different blocks. The only assumption is that, those bits must be retrieved for reporting, as opposed to being computed -- we refer to this requirement as the weak indivisibility assumption. We also describe structures to show that our lower bound is tight up to only a small factor.