Dual encoders perform retrieval by encoding documents and queries into dense low-
dimensional vectors, scoring each document by its inner product with the query. We …

We give two different and simple constructions for dimensionality reduction in ℓ 2 via linear
mappings that are sparse: only an O (ε)-fraction of entries in each column of our embedding …

For any d, n≥ 2 and 1/(min {n, d}) 0.4999<; ε<; 1, we show the existence of a set of n vectors
X⊂ ℝ d such that any embedding f: X→ ℝ m satisfying∀ x, y∈ X,(1-ε)∥ xy∥ 2 2≤∥ f (x)-f …

We prove, using the subspace embedding guarantee in a black box way, that one can
achieve the spectral norm guarantee for approximate matrix multiplication with a …

We show that for n points in d-dimensional Euclidean space, a data oblivious random
projection of the columns onto m∈ O ((log k+ loglog n) ε− 6log1/ε) dimensions is sufficient to …

We present a technical survey on the state of the art approaches in data reduction and the
coreset framework. These include geometric decompositions, gradient methods, random …

We consider algorithmic problems in the setting in which the input data has been partitioned
arbitrarily on many servers. The goal is to compute a function of all the data, and the …

The task of finding heavy hitters is one of the best known and well studied problems in the
area of data streams. One is given a list i 1, i 2,..., im∈[n] and the goal is to identify the items …

We obtain new catalytic algorithms for space-bounded derandomization. In the catalytic
computation model introduced by (Buhrman, Cleve, Koucký, Loff, and Speelman STOC …

This survey article considers methods and algorithms for fast estimation of data
distance/similarity measures from formed real-valued vectors of small dimension. The …