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
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
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Incremental Computation and Maintenance of Temporal Aggregates
Proceedings of the 17th International Conference on Data Engineering
The randomized complexity of maintaining the minimum
Nordic Journal of Computing
Dynamic rectangular intersection with priorities
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Data Structures For One-Dimensional Packet Classification Using Most-Specific-Rule Matching
ISPAN '02 Proceedings of the 2002 International Symposium on Parallel Architectures, Algorithms and Networks
Optimal External Memory Interval Management
SIAM Journal on Computing
I/O-efficient dynamic planar point location
Computational Geometry: Theory and Applications
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
I/O Efficient Dynamic Data Structures for Longest Prefix Queries
SWAT '08 Proceedings of the 11th Scandinavian workshop on Algorithm Theory
Optimal dynamic vertical ray shooting in rectilinear planar subdivisions
ACM Transactions on Algorithms (TALG)
I/O-efficient point location in a set of rectangles
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Clustering lines in high-dimensional space: Classification of incomplete data
ACM Transactions on Algorithms (TALG)
New results on two-dimensional orthogonal range aggregation in external memory
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
A dynamic stabbing-max data structure with sub-logarithmic query time
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
An Optimal Dynamic Data Structure for Stabbing-Semigroup Queries
SIAM Journal on Computing
Optimal splitters for temporal and multi-version databases
Proceedings of the 2013 ACM SIGMOD International Conference on Management of Data
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In this paper we consider the dynamic stabbing-max problem, that is, the problem of dynamically maintaining a set S of n axis-parallel hyper-rectangles in Rd, where each rectangle s ∈ S has a weight w(s) ∈ R, so that the rectangle with the maximum weight containing a query point can be determined efficiently. We develop a linear-size structure for the one-dimensional version of the problem, the interval stabbing-max problem, that answers queries in worst-case O(log n) time and supports updates in amortized O(log n) time. Our structure works in the pointer-machine model of computation and utilizes many ingredients from recently developed external memory structures. Using standard techniques, our one-dimensional structure can be extended to higher dimensions, while paying a logarithmic factor in space, update time, and query time per dimension. Furthermore, our structure can easily be adapted to external memory, where we obtain a linear-size structure that answers queries and supports updates in O(logB n) I/Os, where B is the disk block size.