Approximate medians and other quantiles in one pass and with limited memory
SIGMOD '98 Proceedings of the 1998 ACM SIGMOD international conference on Management of data
SIGMOD '99 Proceedings of the 1999 ACM SIGMOD international conference on Management of data
Space-efficient online computation of quantile summaries
SIGMOD '01 Proceedings of the 2001 ACM SIGMOD international conference on Management of data
Approximate counting of inversions in a data stream
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Deterministic sampling and range counting in geometric data streams
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Effective Computation of Biased Quantiles over Data Streams
ICDE '05 Proceedings of the 21st International Conference on Data Engineering
Space- and time-efficient deterministic algorithms for biased quantiles over data streams
Proceedings of the twenty-fifth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Approximate quantiles and the order of the stream
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
Deterministic sampling and range counting in geometric data streams
ACM Transactions on Algorithms (TALG)
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
Tight lower bounds for selection in randomly ordered streams
Proceedings of the nineteenth 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
Continuously monitoring top-k uncertain data streams: a probabilistic threshold method
Distributed and Parallel Databases
Proceedings of the VLDB Endowment
Aggregate computation over data streams
APWeb'08 Proceedings of the 10th Asia-Pacific web conference on Progress in WWW research and development
Logging every footstep: quantile summaries for the entire history
Proceedings of the 2010 ACM SIGMOD International Conference on Management of data
Counting inversions, offline orthogonal range counting, and related problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
SIAM Journal on Computing
Evaluation of summarization schemes for learning in streams
PKDD'06 Proceedings of the 10th European conference on Principle and Practice of Knowledge Discovery in Databases
Lower bounds for quantile estimation in random-order and multi-pass streaming
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
| Hi-index | 0.00 |
In a recent paper, Ajtai et al. [1] give a streaming algorithm to count the number of inversions in a stream Lε[m]n using two passes and O(ε−1-√n log n(log m + log n)) space. Here, we present a simple randomized streaming algorithm for the same problem that uses one pass and O(ε−3 log2 n log m) space. Our algorithm is based on estimating quantiles of the items already seen in the stream, and using that to estimate the number of inversions involving each element.