Approximate counting: a detailed analysis
BIT - Ellis Horwood series in artificial intelligence
A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
A survey of adaptive sorting algorithms
ACM Computing Surveys (CSUR)
Exploiting few inversions when sorting: sequential and parallel algorithms
Theoretical Computer Science
Communication complexity
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Journal of Algorithms - Special issue on SODA '95 papers
Sorting Permutations by Reversals and Eulerian Cycle Decompositions
SIAM Journal on Discrete Mathematics
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
External memory algorithms
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Counting large numbers of events in small registers
Communications of the ACM
Rank aggregation methods for the Web
Proceedings of the 10th international conference on World Wide Web
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Optimal Algorithms for List Indexing and Subset Rank
WADS '89 Proceedings of the Workshop on Algorithms and Data Structures
An Approximate L1-Difference Algorithm for Massive Data Streams
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Pass efficient algorithms for approximating large matrices
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Better streaming algorithms for clustering problems
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Exploiting k-constraints to reduce memory overhead in continuous queries over data streams
ACM Transactions on Database Systems (TODS)
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Range-Efficient Computation of F" over Massive Data Streams
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
Continuously maintaining order statistics over data streams: extended abstract
ADC '07 Proceedings of the eighteenth conference on Australasian database - Volume 63
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
On distance to monotonicity and longest increasing subsequence of a data stream
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Partition Arguments in Multiparty Communication Complexity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Aggregate computation over data streams
APWeb'08 Proceedings of the 10th Asia-Pacific web conference on Progress in WWW research and development
Near-optimal sublinear time algorithms for Ulam distance
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Counting inversions, offline orthogonal range counting, and related problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Partition arguments in multiparty communication complexity
Theoretical Computer Science
SIAM Journal on Computing
Finding longest increasing and common subsequences in streaming data
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Edit distance to monotonicity in sliding windows
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
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(MATH) Inversions are used as a fundamental quantity to measure the sortedness of data, to evaluate different ranking methods for databases, and in the context of rank aggregation. Considering the volume of the data sets in these applications, the data stream model {14, 2] is a natural setting to design efficient algorithms.We obtain a suite of space-efficient streaming algorithms for approximating the number of inversions in a permutation. The best space bound we achieve is $O(\log n \log \log n)$ through a deterministic algorithm. In contrast, we derive an $\Omega(n)$ lower bound for randomized exact computation for this problem; thus approximation is essential.(MATH) We also consider two generalizations of this problem: (1) approximating the number of inversions between two permutations, for which we obtain a randomized $O(\sqrt{n} \log n)$-space algorithm, and (2) approximating the number of inversions in a general list, for which we obtain a randomized $O(\sqrt{n} \log^2 n)$-space two-pass algorithm. In contrast, we derive $\Omega(n)$-space lower bounds for deterministic approximate computation for these problems; thus both randomization and approximation are essential.All our algorithms use only O(log n) time per data item.