New asymptotics for bipartite Tura´n numbers
Journal of Combinatorial Theory Series A
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
Reductions in streaming algorithms, with an application to counting triangles in graphs
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
An Information Statistics Approach to Data Stream and Communication Complexity
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On finding common neighborhoods in massive graphs
Theoretical Computer Science
An Approximate L1-Difference Algorithm for Massive Data Streams
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
An improved data stream algorithm for frequency moments
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal approximations of the frequency moments of data streams
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Counting triangles in data streams
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
New streaming algorithms for counting triangles in graphs
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
On the streaming complexity of computing local clustering coefficients
Proceedings of the sixth ACM international conference on Web search and data mining
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The last decade witnessed the extensive studies of algorithms for data streams. In this model, the input is given as a sequence of items passing only once or a few times, and we are required to compute (often approximately) some statistical quantity using a small amount of space. While many lower bounds on the space complexity have been proved for various tasks, almost all of them were done by reducing the problems to the cases where the desired statistical quantity is at one extreme end. For example, the lower bound of triangle-approximating was showed by reducing the problem to distinguishing between graphs without triangle and graphs with only one triangle. However, data in many practical applications are not in the extreme, and/or usually we are interested in computing the statistical quantity only if it is in some range (and otherwise reporting "too large" or "too small"). This paper takes this practical relaxation into account by putting the computed quantity itself into themeasure of space complexity. It turns out that all three possible types of dependence of the space complexity on the computed quantity exist: as the quantity goes from one end to the other, the space complexity can goes from max to min, remains at max, or goes to somewhere between.