On relations between arrays of processing elements of different dimensionality

We are examining the power of $d$-dimensional arrays of processing elements in view of a special kind of structural complexity. In particular simulation techniques are shown, which allow to reduce the dimension at an increased cost of time only. Conversely, it is not possible to regain the speed by increasing the dimension. Moreover, we demonstrate that increasing the computation time (just by a constant factor) can have a more favorable effect than increasing the dimension (arbitrari

A Survey on Array Storage, Query Languages, and Systems

Since scientific investigation is one of the most important providers of massive amounts of ordered data, there is a renewed interest in array data processing in the context of Big Data. To the best of our knowledge, a unified resource that summarizes and analyzes array processing research over its long existence is currently missing. In this survey, we provide a guide for past, present, and future research in array processing. The survey is organized along three main topics. Array storage discusses all the aspects related to array partitioning into chunks. The identification of a reduced set of array operators to form the foundation for an array query language is analyzed across multiple such proposals. Lastly, we survey real systems for array processing. The result is a thorough survey on array data storage and processing that should be consulted by anyone interested in this research topic, independent of experience level. The survey is not complete though. We greatly appreciate pointers towards any work we might have forgotten to mention.Comment: 44 page

Channel Covariance Matrix Estimation via Dimension Reduction for Hybrid MIMO MmWave Communication Systems

Hybrid massive MIMO structures with lower hardware complexity and power consumption have been considered as a potential candidate for millimeter wave (mmWave) communications. Channel covariance information can be used for designing transmitter precoders, receiver combiners, channel estimators, etc. However, hybrid structures allow only a lower-dimensional signal to be observed, which adds difficulties for channel covariance matrix estimation. In this paper, we formulate the channel covariance estimation as a structured low-rank matrix sensing problem via Kronecker product expansion and use a low-complexity algorithm to solve this problem. Numerical results with uniform linear arrays (ULA) and uniform squared planar arrays (USPA) are provided to demonstrate the effectiveness of our proposed method

FLASH: Randomized Algorithms Accelerated over CPU-GPU for Ultra-High Dimensional Similarity Search

We present FLASH (\textbf{F}ast \textbf{L}SH \textbf{A}lgorithm for \textbf{S}imilarity search accelerated with \textbf{H}PC), a similarity search system for ultra-high dimensional datasets on a single machine, that does not require similarity computations and is tailored for high-performance computing platforms. By leveraging a LSH style randomized indexing procedure and combining it with several principled techniques, such as reservoir sampling, recent advances in one-pass minwise hashing, and count based estimations, we reduce the computational and parallelization costs of similarity search, while retaining sound theoretical guarantees. We evaluate FLASH on several real, high-dimensional datasets from different domains, including text, malicious URL, click-through prediction, social networks, etc. Our experiments shed new light on the difficulties associated with datasets having several million dimensions. Current state-of-the-art implementations either fail on the presented scale or are orders of magnitude slower than FLASH. FLASH is capable of computing an approximate k-NN graph, from scratch, over the full webspam dataset (1.3 billion nonzeros) in less than 10 seconds. Computing a full k-NN graph in less than 10 seconds on the webspam dataset, using brute-force ($n^2D$), will require at least 20 teraflops. We provide CPU and GPU implementations of FLASH for replicability of our results