A survey of adaptive sorting algorithms
ACM Computing Surveys (CSUR)
Theoretical Computer Science - Special issue on complexity theory and the theory of algorithms as developed in the CIS
The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Approximate counting of inversions in a data stream
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Permutation Editing and Matching via Embeddings
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Continuously Maintaining Quantile Summaries of the Most Recent N Elements over a Data Stream
ICDE '04 Proceedings of the 20th International Conference on Data Engineering
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
On distance to monotonicity and longest increasing subsequence of a data stream
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Time-decaying aggregates in out-of-order streams
Proceedings of the twenty-seventh ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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
Detecting and exploiting near-sortedness for efficient relational query evaluation
Proceedings of the 14th International Conference on Database Theory
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Given a stream of items each associated with a numerical value, its edit distance to monotonicity is the minimum number of items to remove so that the remaining items are non-decreasing with respect to the numerical value. The space complexity of estimating the edit distance to monotonicity of a data stream is becoming well-understood over the past few years. Motivated by applications on network quality monitoring, we extend the study to estimating the edit distance to monotonicity of a sliding window covering the w most recent items in the stream for any w≥1. We give a deterministic algorithm which can return an estimate within a factor of (4+ε) using $O(\frac{1}{\epsilon ^2} \log^2(\epsilon w))$ space. We also extend the study in two directions. First, we consider a stream where each item is associated with a value from a partial ordered set. We give a randomized (4+ε)-approximate algorithm using $O(\frac{1}{\epsilon^2} \log \epsilon^2 w \log w)$ space. Second, we consider an out-of-order stream where each item is associated with a creation time and a numerical value, and items may be out of order with respect to their creation times. The goal is to estimate the edit distance to monotonicity with respect to the numerical value of items arranged in the order of creation times. We show that any randomized constant-approximate algorithm requires linear space.