The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Min-wise independent permutations (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Efficient search for approximate nearest neighbor in high dimensional spaces
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Tracking join and self-join sizes in limited storage
PODS '99 Proceedings of the eighteenth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Synopsis data structures for massive data sets
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
An Information-Theoretic Treatment of Random-Self-Reducibility (Extended Abstract)
STACS '97 Proceedings of the 14th Annual Symposium on Theoretical Aspects of Computer Science
An Approximate L1-Difference Algorithm for Massive Data Streams
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Finding longest increasing and common subsequences in streaming data
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Testing Closeness of Discrete Distributions
Journal of the ACM (JACM)
Decision support based needs assessment for cancer patients
HIKM '11 Proceedings of the Fourth Australasian Workshop on Health Informatics and Knowledge Management - Volume 120
Real time processing of data from patient biodevices
HIKM '11 Proceedings of the Fourth Australasian Workshop on Health Informatics and Knowledge Management - Volume 120
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Several recent papers have shown how to approximate the difference Σi|ai - bi| or Σ|ai - bi|2 between two functions, when the function values ai and bi are given in a data stream, and their order is chosen by an adversary. These algorithms use little space (much less than would be needed to store the entire stream) and little time to process each item in the stream and give approximations with small relative error. Using different techniques, we show how to approximate the Lp- difference Σi |ai-bi|p for any rational-valued p ∈ (0; 2), with comparable efficiency and error. We also show how to approximate Σi |ai - bi|p for larger values of p but with a worse error guarantee. These results can be used to assess the difference between two chronologically or physically separated massive data sets, making one quick pass over each data set, without buffering the data or requiring the data source to pause.