Communication complexity
Quantum vs. classical communication and computation
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Las Vegas is better than determinism in VLSI and distributed computing (Extended Abstract)
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
Algorithms for dynamic geometric problems over data streams
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Space efficient mining of multigraph streams
Proceedings of the twenty-fourth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
An improved data stream summary: the count-min sketch and its applications
Journal of Algorithms
Data streams: algorithms and applications
Foundations and Trends® in Theoretical Computer Science
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
Overcoming the l1 non-embeddability barrier: algorithms for product metrics
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
The Data Stream Space Complexity of Cascaded Norms
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Efficient Sketches for Earth-Mover Distance, with Applications
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Sublinear Optimization for Machine Learning
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
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We study the space complexity of randomized streaming algorithms that provide one-sided approximation guarantees; e.g., the algorithm always returns an overestimate of the function being computed, and with high probability, the estimate is not too far from the true answer. We also study algorithms which always provide underestimates. We also give lower bounds for several one-sided estimators that match the deterministic space complexity, thus showing that to get a spaceefficient solution, two-sided approximations are sometimes necessary. For some of these problems, including estimating the longest increasing sequence in a stream, and estimating the Earth Mover Distance, these are the first lower bounds for randomized algorithms of any kind. We show that for several problems, including estimating the radius of theMinimum Enclosing Ball (MEB), one-sided estimation is possible. We provide a natural function for which the space for one-sided estimation is asymptotically less than the space required for deterministic algorithms, but more than what is required for general randomized algorithms. What if an algorithm has a one-sided approximation from both sides? In this case, we show the problem has what we call a Las Vegas streaming algorithm. We show that even for two-pass algorithms, a quadratic improvement in space is possible and give a natural problem, counting non-isolated vertices in a graph, which achieves this separation.