The input/output complexity of sorting and related problems
Communications of the ACM
An optimal algorithm for selection in a min-heap
Information and Computation
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
Range Top/Bottom k Queries in OLAP Sparse Data Cubes
DEXA '01 Proceedings of the 12th International Conference on Database and Expert Systems Applications
Optimal dynamic interval management in external memory
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Incremental computation and maintenance of temporal aggregates
The VLDB Journal — The International Journal on Very Large Data Bases
Efficient Process of Top-k Range-Sum Queries over Multiple Streams with Minimized Global Error
IEEE Transactions on Knowledge and Data Engineering
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Ordered and unordered top-K range reporting in large data sets
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
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In the top-K range reporting problem, the dataset contains N points in the real domain ℜ, each of which is associated with a real-valued score. Given an interval x1,x2 in ℜ and an integer K≤ N, a query returns the K points in x1,x2 having the smallest scores. We want to store the dataset in a structure so that queries can be answered efficiently. In the external memory model, the state of the art is a static structure that consumes O(N/B) space, answers a query in O(logB N + K/B) time, and can be constructed in O(N + (N log N / B) log M/B (N/B)) time, where B is the size of a disk block, and M the size of memory. We present a fully-dynamic structure that retains the same space and query bounds, and can be updated in O(log2B N) amortized time per insertion and deletion. Our structure can be constructed in O((N/B) log M/B (N/B)) time.