Fast Manhattan sketches in data streams
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Information complexity: a tutorial
Proceedings of the twenty-ninth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Lower bounds for edit distance and product metrics via Poincaré-type inequalities
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Coresets and sketches for high dimensional subspace approximation problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
1-pass relative-error Lp-sampling with applications
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
On the exact space complexity of sketching and streaming small norms
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Tight bounds for Lp samplers, finding duplicates in streams, and related problems
Proceedings of the thirtieth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
Near-optimal private approximation protocols via a black box transformation
Proceedings of the forty-third annual ACM symposium on Theory of 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
Estimating hybrid frequency moments of data streams
Journal of Combinatorial Optimization
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We consider the problem of estimating cascaded aggregates over a matrix presented as a sequence of updates in a data stream. A cascaded aggregate P 卤Q is defined by evaluating aggregate Q repeatedly over each row of the matrix, and then evaluating aggregate P over the resulting vector of values. This problem was introduced by Cormode andMuthukrishnan, PODS, 2005 [CM]. We analyze the space complexity of estimating cascaded norms on an n 拢d matrix to within a small relative error. Let Lp denote the p-th norm, where p is a non-negative integer. We abbreviate the cascaded normLk 卤Lp by Lk,p . (1) For any constant k 赂 p 赂 2, we obtain a 1-pass e O(n1隆2/kd1隆2/p )-space algorithm for estimating Lk,p . This is optimal up to polylogarithmic factors and resolves an open question of [CM] regarding the space complexity of L4,2. We also obtain 1-pass space-optimal algorithms for estimating L1,k and Lk,1. (2)We prove a space lower bound of (n1隆1/k ) on estimating Lk,0 and Lk,1, resolving an open question due to Indyk, IITK Data StreamsWorkshop (Problem 8), 2006. We also resolve two more questions of [CM] concerning Lk,2 estimation and block heavy hitter problems. Ganguly, Bansal and Dube (FAW, 2008) claimed an e O(1)-space algorithm for estimating Lk,p for any k,p 2 [0,2]. Our lower bounds show this claimis incorrect.