We consider the Max-Cut problem, asking how much space is needed by a streaming algorithm in order to estimate the value of the maximum cut in a graph. This problem has been extensively studied over the last decade, and we now have a near-optimal lower bound for one-pass streaming algorithms, ... more >>>

Rounding has proven to be a fundamental tool in theoretical computer science. By observing that rounding and partitioning of $\mathbb{R}^d$ are equivalent, we introduce the following natural partition problem which we call the secluded hypercube partition problem: Given $k\in\mathbb{N}$ (ideally small) and $\epsilon>0$ (ideally large), is there a partition of ... more >>>

Deep neural networks are the dominant machine learning model. We show that this model is missing a crucial complexity parameter. Today, the standard neural network (NN) model is a circuit whose gates (neurons) are ReLU units. The complexity of a NN is quantified by the depth (number of layers) and ... more >>>