Streaming Algorithms with One-Sided Estimation

Abstract. 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 space-efficient 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 the Minimum Enclosing Ball (MEB), one-sided estimation is possible. We provide a natural function for which the space for one-sided estimation is asymptotically less t...

• Type: Journal
• Year: 2011
• Where: APPROX
• Authors: Joshua Brody, David P. Woodruff
• Keywords: Algorithms, APPROX 2011, Approximation Guarantees, Deterministic Algorithms, Study Algorithms