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We study the heavy hitters and related sparse recovery problems in the low-failure probability regime. This regime is not well-understood, and has only been studied for non-adaptive schemes. The main previous work is one on sparse recovery by Gilbert et al.(ICALP13). We recognize an error in their analysis, improve their results, and contribute new non-adaptive and adaptive sparse recovery algorithms, as well as provide upper and lower bounds for the heavy hitters problem with low failure probability.
We study the distinct elements and $ell_p$-heavy hitters problems in the sliding window model, where only the most recent $n$ elements in the data stream form the underlying set. We first introduce the composable histogram, a simple twist on the expo
In the long-studied problem of combinatorial group testing, one is asked to detect a set of $k$ defective items out of a population of size $n$, using $m ll n$ disjunctive measurements. In the non-adaptive setting, the most widely used combinatorial
Finding heavy hitters has been of vital importance in network measurement. Among all the recent works in finding heavy hitters, the Elastic sketch achieves the highest accuracy and fastest speed. However, we find that there is still room for improvem
Suppose that a solution $widetilde{mathbf{x}}$ to an underdetermined linear system $mathbf{b} = mathbf{A} mathbf{x}$ is given. $widetilde{mathbf{x}}$ is approximately sparse meaning that it has a few large components compared to other small entries.
We provide a randomized linear time approximation scheme for a generic problem about clustering of binary vectors subject to additional constrains. The new constrained clustering problem encompasses a number of problems and by solving it, we obtain t