On the distributional complexity of disjointness
Theoretical Computer Science
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Space lower bounds for distance approximation in the data stream model
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
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
Simpler algorithm for estimating frequency moments of data streams
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
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
Lower bounds for randomized read/write stream algorithms
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
On the Value of Multiple Read/Write Streams for Approximating Frequency Moments
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Lower bounds for processing data with few random accesses to external memory
Journal of the ACM (JACM)
Hellinger Strikes Back: A Note on the Multi-party Information Complexity of AND
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
An optimal lower bound on the communication complexity of gap-hamming-distance
Proceedings of the forty-third annual ACM symposium on Theory of computing
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We consider the read/write streams model, an extension of the standard data stream model in which an algorithm can create and manipulate multiple read/write streams in addition to its input data stream. Like the data stream model, the most important parameter for this model is the amount of internal memory used by such an algorithm. The other key parameters are the number of streams the algorithm uses and the number of passes it makes on these streams. We consider how the addition of multiple streams impacts the ability of algorithms to approximate the frequency moments of the input stream. We show that any randomized read/write stream algorithm with a fixed number of streams and a sublogarithmic number of passes that produces a constant factor approximation of the k-th frequency moment Fk of an input sequence of length of at most N from {1,..., N} requires space Ω(N 1−4/k−δ) for any δ 0. For comparison, it is known that with a single read-only one-pass data stream there is a randomized constant-factor approximation for Fk using Õ(N1−2/k) space, and that by sorting, which can be done deterministically in O(log N) passes using 3 read/write streams, Fk can be computed exactly. Therefore, although the ability to manipulate multiple read/write streams can add substantial power to the data stream model, with a sublogarithmic number of passes this does not significantly improve the ability to approximate higher frequency moments efficiently. We obtain our results by showing a new connection between the read/write streams model and the multiparty number-in-hand communication model.