Unbiased bits from sources of weak randomness and probabilistic communication complexity
SIAM Journal on Computing - Special issue on cryptography
SIAM Journal on Computing
On the distributional complexity of disjointness
Theoretical Computer Science
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Time-space trade-off lower bounds for randomized computation of decision problems
Journal of the ACM (JACM)
Tight Lower Bounds for the Distinct Elements Problem
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Optimal space lower bounds for all frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for new computational models
Efficient algorithms for new computational models
On the Streaming Model Augmented with a Sorting Primitive
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for sorting with few random accesses to external memory
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Randomized computations on large data sets: tight lower bounds
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Tight lower bounds for query processing on streaming and external memory data
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Machine models and lower bounds for query processing
Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Theoretical Computer Science
Lower bounds for processing data with few random accesses to external memory
Journal of the ACM (JACM)
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Trading off space for passes in graph streaming problems
ACM Transactions on Algorithms (TALG)
Proceedings of the forty-second ACM symposium on Theory of computing
Machine models for query processing
ACM SIGMOD Record
The Value of Multiple Read/Write Streams for Approximating Frequency Moments
ACM Transactions on Computation Theory (TOCT)
Grammar-based compression in a streaming model
LATA'10 Proceedings of the 4th international conference on Language and Automata Theory and Applications
Validating XML documents in the streaming model with external memory
Proceedings of the 15th International Conference on Database Theory
Validating XML documents in the streaming model with external memory
ACM Transactions on Database Systems (TODS) - Invited papers issue
Tradeoff lower lounds for stack machines
Computational Complexity
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Motivated by the capabilities of modern storage architectures, we consider the following generalization of the data stream model where the algorithm has sequential access to multiple streams. Unlike the data stream model, where the stream is read only, in this new model (introduced in [8,9]) the algorithms can also write onto streams. There is no limit on the size of the streams but the number of passes made on the streams is restricted. On the other hand, the amount of internal memory used by the algorithm is scarce, similar to data stream model. We resolve the main open problem in [7] of proving lower bounds in this model for algorithms that are allowed to have 2-sided error. Previously, such lower bounds were shown only for deterministic and 1-sided error randomized algorithms [9,7]. We consider the classical set disjointness problemthat has proved to be invaluable for deriving lower bounds for many other problems involving data streams and other randomized models of computation. For this problem, we show a near-linear lower bound on the size of the internal memory used by a randomized algorithm with 2-sided error that is allowed to have o(log N/log log N) passes over the streams. This bound is almost optimal sincethere is a simple algorithm that can solve this problem using logarithmic memory if the number of passes over the streams. Applications include near-linear lower bounds onthe internal memory for well-known problems in the literature:(1) approximately counting the number of distinct elements in the input (F0);(2) approximating the frequency of the mod of an input sequence(F*∞);(3) computing the join of two relations; and (4) deciding if some node of an XML document matches an XQuery (or XPath) query. Our techniques involve a novel direct-sum type of argument that yields lower bounds for many other problems. Our results asymptotically improve previously known bounds for any problem even in deterministic and 1-sided error models of computation.