LRM-Trees: Compressed Indices, Adaptive Sorting, and Compressed Permutations

LRM-Trees are an elegant way to partition a sequence of values into sorted consecutive blocks, and to express the relative position of the first element of each block within a previous block. They were used to encode ordinal trees and to index integer arrays in order to support range minimum queries on them. We describe how they yield many other convenient results in a variety of areas, from data structures to algorithms: some compressed succinct indices for range minimum queries; a new adaptive sorting algorithm; and a compressed succinct data structure for permutations supporting direct and indirect application in time all the shortest as the permutation is compressible.Comment: 13 pages, 1 figur

Using sources of opportunity to compensate for receiver mismatch in HF arrays

© 2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.The spatial processing performance of adaptive sensor arrays is often limited by the nonidentical frequency responses of the receivers in the array over the passband of interest. Addressed here is the problem of estimating digital compensation for mismatches between receiver passbands in high frequency (HF) antenna arrays using interference sources of opportunity. A mathematical model of ionospherically-propagated multipath HF interference is used to develop an adaptive algorithm which estimates the receiver frequency response corrections for each receiver. The effectiveness of the proposed algorithm is experimentally demonstrated and compared against (1) a commonly used least squares technique, and (2) a highly accurate calibration system using data collected by the receiving antenna array of the Jindalee over-the-horizon radar near Alice Springs in central AustraliaFabrizio, G.A.; Gray, D.A.; Turley, M.D

Performance and Optimization Abstractions for Large Scale Heterogeneous Systems in the Cactus/Chemora Framework

We describe a set of lower-level abstractions to improve performance on modern large scale heterogeneous systems. These provide portable access to system- and hardware-dependent features, automatically apply dynamic optimizations at run time, and target stencil-based codes used in finite differencing, finite volume, or block-structured adaptive mesh refinement codes. These abstractions include a novel data structure to manage refinement information for block-structured adaptive mesh refinement, an iterator mechanism to efficiently traverse multi-dimensional arrays in stencil-based codes, and a portable API and implementation for explicit SIMD vectorization. These abstractions can either be employed manually, or be targeted by automated code generation, or be used via support libraries by compilers during code generation. The implementations described below are available in the Cactus framework, and are used e.g. in the Einstein Toolkit for relativistic astrophysics simulations

Algorithmic patterns for H\mathcal{H}-matrices on many-core processors

In this work, we consider the reformulation of hierarchical ($\mathcal{H}$) matrix algorithms for many-core processors with a model implementation on graphics processing units (GPUs). $\mathcal{H}$ matrices approximate specific dense matrices, e.g., from discretized integral equations or kernel ridge regression, leading to log-linear time complexity in dense matrix-vector products. The parallelization of $\mathcal{H}$ matrix operations on many-core processors is difficult due to the complex nature of the underlying algorithms. While previous algorithmic advances for many-core hardware focused on accelerating existing $\mathcal{H}$ matrix CPU implementations by many-core processors, we here aim at totally relying on that processor type. As main contribution, we introduce the necessary parallel algorithmic patterns allowing to map the full $\mathcal{H}$ matrix construction and the fast matrix-vector product to many-core hardware. Here, crucial ingredients are space filling curves, parallel tree traversal and batching of linear algebra operations. The resulting model GPU implementation hmglib is the, to the best of the authors knowledge, first entirely GPU-based Open Source $\mathcal{H}$ matrix library of this kind. We conclude this work by an in-depth performance analysis and a comparative performance study against a standard $\mathcal{H}$ matrix library, highlighting profound speedups of our many-core parallel approach

Breaking the O(n^2) Bit Barrier: Scalable Byzantine agreement with an Adaptive Adversary

We describe an algorithm for Byzantine agreement that is scalable in the sense that each processor sends only $\tilde{O}(\sqrt{n})$ bits, where $n$ is the total number of processors. Our algorithm succeeds with high probability against an \emph{adaptive adversary}, which can take over processors at any time during the protocol, up to the point of taking over arbitrarily close to a 1/3 fraction. We assume synchronous communication but a \emph{rushing} adversary. Moreover, our algorithm works in the presence of flooding: processors controlled by the adversary can send out any number of messages. We assume the existence of private channels between all pairs of processors but make no other cryptographic assumptions. Finally, our algorithm has latency that is polylogarithmic in $n$. To the best of our knowledge, ours is the first algorithm to solve Byzantine agreement against an adaptive adversary, while requiring $o(n^{2})$ total bits of communication