The input/output complexity of sorting and related problems
Communications of the ACM
A lower bound for the dictionary problem under a hashing model
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Dynamic Perfect Hashing: Upper and Lower Bounds
SIAM Journal on Computing
The log-structured merge-tree (LSM-tree)
Acta Informatica
Heaps and heapsort on secondary storage
Theoretical Computer Science
Journal of the ACM (JACM)
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Space/time trade-offs in hash coding with allowable errors
Communications of the ACM
On the cell probe complexity of membership and perfect hashing
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Lower bounds for external memory dictionaries
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Novel Index Supporting High Volume Data Warehouse Insertion
VLDB '99 Proceedings of the 25th International Conference on Very Large Data Bases
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Journal of Algorithms
Logarithmic Lower Bounds in the Cell-Probe Model
SIAM Journal on Computing
Why simple hash functions work: exploiting the entropy in a data stream
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Probabilistic computations: Toward a unified measure of complexity
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
On the complexity of a game related to the dictionary problem
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Optimality in External Memory Hashing
Algorithmica
Algorithms and Data Structures for External Memory
Algorithms and Data Structures for External Memory
Dynamic indexability and lower bounds for dynamic one-dimensional range query indexes
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Dynamic external hashing: the limit of buffering
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
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
Using hashing to solve the dictionary problem
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We study the dynamic membership problem, one of the most fundamental data structure problems, in the cell probe model with an arbitrary cell size. We consider a cell probe model equipped with a cache that consists of at least a constant number of cells; reading or writing the cache is free of charge. For nearly all common data structures, it is known that with sufficiently large cells together with the cache, we can significantly lower the amortized update cost to o(1). In this paper, we show that this is not the case for the dynamic membership problem. Specifically, for any deterministic membership data structure under a random input sequence, if the expected average query cost is no more than 1+δ for some small constant δ, we prove that the expected amortized update cost must be at least Ω(1), namely, it does not benefit from large block writes (and a cache). The space the structure uses is irrelevant to this lower bound. We also extend this lower bound to randomized membership structures, by using a variant of Yao's minimax principle. Finally, we show that the structure cannot do better even if it is allowed to answer a query mistakenly with a small constant probability.