The probabilistic communication complexity of set intersection
SIAM Journal on Discrete Mathematics
The space complexity of approximating the frequency moments
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
Communication complexity
On data structures and asymmetric communication complexity
Journal of Computer and System Sciences
Algorithms for the Longest Common Subsequence Problem
Journal of the ACM (JACM)
On randomized one-round communication complexity
Computational Complexity
A fast algorithm for computing longest common subsequences
Communications of the ACM
Enumerating longest increasing subsequences and patience sorting
Information Processing Letters
Analysis of Algorithms and Data and Structures
Analysis of Algorithms and Data and Structures
Data streams: algorithms and applications
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Estimating the sortedness of a data stream
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Finding longest increasing and common subsequences in streaming data
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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
Effective Computations on Sliding Windows
SIAM Journal on Computing
SIAM Journal on Computing
Efficient communication protocols for deciding edit distance
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Space-bounded communication complexity
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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We consider the communication complexity of finding the longest increasing subsequence (LIS) of a string shared between two parties. We prove tight bounds for the space complexity of randomized one-pass streaming algorithms for this problem. Our bounds are parameterized in terms of the LIS of the inputs. This resolves an open question in [19]. We also give the first bounds for approximating the LIS and its length. Next, we consider the communication complexity of finding the longest common subsequece (LCS) of two strings held by different parties, as well as the problem of approximating its length. We improve the existing lower bounds for these problems, even in the most difficult case when both parties have a permutation of N symbols. Our results yield tight space bounds for multipass deterministic streaming algorithms. For randomized mutlipass algorithms, our bounds are tight up to a logarithmic factor.