We consider relative error low rank approximation of tensors with respect to the Frobenius norm. Namely, given an order-q tensor A \in \mathbb{R}^{\prod_{i=1}^q n_i}, output a rank-k tensor B for which \|A-B\|_F^2 \leq (1+\epsilon) {\rm OPT}, where {\rm OPT} = \inf_{\textrm{rank-}k~A'} \|A-A'\|_F^2. Despite much success on obtaining relative error low ... more >>>

Consider a large database of n data items that need to be stored using m servers.
We study how to encode information so that a large number k of read requests can be performed \textit{in parallel} while the rate remains constant (and ideally approaches one).
This problem is equivalent ... more >>>