Space-optimal heavy hitters with strong error bounds
Proceedings of the twenty-eighth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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Approximate sparse recovery: optimizing time and measurements
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Space-optimal heavy hitters with strong error bounds
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Theoretical Computer Science
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Proceedings of the forty-third annual ACM symposium on Theory of computing
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Approximate Sparse Recovery: Optimizing Time and Measurements
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SIAM Journal on Matrix Analysis and Applications
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ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
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We consider the *approximate sparse recovery problem*, where the goal is to (approximately) recover a high-dimensional vector x from Rn from its lower-dimensional *sketch* Ax from Rm.Specifically, we focus on the sparse recovery problem in the L1 norm: for a parameter k, given the sketch Ax, compute an approximation x' of x such that the L1 approximation error | |x-x'| | is close to minimum of | |x-x*| | over all vectors x* with at most k terms. The sparse recovery problem has been subject to extensive research over the last few years.Many solutions to this problem have been discovered, achieving different trade-offs between various attributes, such as the sketch length, encoding and recovery times.In this paper we provide a sparse recovery scheme which achieves close to optimal performance on virtually all attributes. In particular, this is the first recovery scheme that guarantees k log(n/k) sketch length, and near-linear n log (n/k) recovery time *simultaneously*. It also features low encoding and update times, and is noise-resilient.