Random sampling with a reservoir
ACM Transactions on Mathematical Software (TOMS)
Algorithms on strings, trees, and sequences: computer science and computational biology
Algorithms on strings, trees, and sequences: computer science and computational biology
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
Approximate counting of inversions in a data stream
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Monotonicity testing over general poset domains
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Models and issues in data stream systems
Proceedings of the twenty-first ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
The string edit distance matching problem with moves
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Lower bounds for embedding edit distance into normed spaces
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A sublinear algorithm for weakly approximating edit distance
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
An information statistics approach to data stream and communication complexity
Journal of Computer and System Sciences - Special issue on FOCS 2002
Approximating Edit Distance Efficiently
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Low distortion embeddings for edit distance
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Nonembeddability theorems via Fourier analysis
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Improved lower bounds for embeddings into L1
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Space-efficient Relative Error Order Sketch over Data Streams
ICDE '06 Proceedings of the 22nd International Conference on Data Engineering
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
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
Efficient learning algorithms for changing environments
ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
Proceedings of the VLDB Endowment
Near-optimal sublinear time algorithms for Ulam distance
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Effective Computations on Sliding Windows
SIAM Journal on Computing
The Computational Hardness of Estimating Edit Distance
SIAM Journal on Computing
Streaming algorithms with one-sided estimation
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
SIAM Journal on Computing
A note on randomized streaming space bounds for the longest increasing subsequence problem
Information Processing Letters
Edit distance to monotonicity in sliding windows
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Efficient communication protocols for deciding edit distance
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Streaming computations with a loquacious prover
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Hi-index | 0.00 |
The distance to monotonicity of a sequence is the minimum number of edit operations required to transform the sequence into an increasing order; this measure is complementary to the length of the longest increasing subsequence (LIS). We address the question of estimating these quantities in the one-pass data stream model and present the first sub-linear space algorithms for both problems. We first present O(√n)-space deterministic algorithms that approximate the distance to monotonicity and the LIS to within a factor that is arbitrarily close to 1. We also show a lower bound of Ω(n) on the space required by any randomized algorithm to compute the LIS (or alternatively the distance from monotonicity) exactly, demonstrating that approximation is necessary for sub-linear space computation; this bound improves upon the existing lower bound of Ω(√n) [LNVZ06]. Our main result is a randomized algorithm that uses only O(log2 n) space and approximates the distance to monotonicity to within a factor that is arbitrarily close to 4. In contrast, we believe that any significant reduction in the space complexity for approximating the length of the LIS is considerably hard. We conjecture that any deterministic (1 + ε) approximation algorithm for LIS requires Ω (√n) space, and as a step towards this conjecture, prove a space lower bound of Ω(√n) for a restricted yet natural class of deterministic algorithms.