An exploration of graph algorithms and graph databases

With data becoming larger in quantity, the need for complex, efficient algorithms to solve computationally complex problems has become greater. In this thesis we evaluate a selection of graph algorithms; we provide a novel algorithm for solving and approximating the Longest Simple Cycle problem, as well as providing novel implementations of other graph algorithms in graph database systems.The first area of exploration is finding the Longest Simple Cycle in a graph problem. We propose two methods of finding the longest simple cycle. The first method is an exact approach based on a flow-based Integer Linear Program. The second is a multi-start local search heuristic which uses a simple depth-first search as a basis for a cycle, and improves this with four perturbation operators.Secondly, we focus on implementing the Minimum Dominating Set problem into graph database systems. An unoptimised greedy heuristic solution to the Minimum Dominating Set problem is implemented into a client-server system using a declarative query language, an embedded database system using an imperative query language and a high level language as a direct comparison. The performance of the graph back-end on the database systems is evaluated. The language expressiveness of the query languages is also explored. We identify limitations of the query methods of the database system, and propose a function that increases the functionality of the queries

Minimum entropy restoration using FPGAs and high-level techniques

One of the greatest perceived barriers to the widespread use of FPGAs in image processing is the difficulty for application specialists of developing algorithms on reconfigurable hardware. Minimum entropy deconvolution (MED) techniques have been shown to be effective in the restoration of star-field images. This paper reports on an attempt to implement a MED algorithm using simulated annealing, first on a microprocessor, then on an FPGA. The FPGA implementation uses DIME-C, a C-to-gates compiler, coupled with a low-level core library to simplify the design task. Analysis of the C code and output from the DIME-C compiler guided the code optimisation. The paper reports on the design effort that this entailed and the resultant performance improvements

PURIFY: a new approach to radio-interferometric imaging

In a recent article series, the authors have promoted convex optimization algorithms for radio-interferometric imaging in the framework of compressed sensing, which leverages sparsity regularization priors for the associated inverse problem and defines a minimization problem for image reconstruction. This approach was shown, in theory and through simulations in a simple discrete visibility setting, to have the potential to outperform significantly CLEAN and its evolutions. In this work, we leverage the versatility of convex optimization in solving minimization problems to both handle realistic continuous visibilities and offer a highly parallelizable structure paving the way to significant acceleration of the reconstruction and high-dimensional data scalability. The new algorithmic structure promoted relies on the simultaneous-direction method of multipliers (SDMM), and contrasts with the current major-minor cycle structure of CLEAN and its evolutions, which in particular cannot handle the state-of-the-art minimization problems under consideration where neither the regularization term nor the data term are differentiable functions. We release a beta version of an SDMM-based imaging software written in C and dubbed PURIFY (http://basp-group.github.io/purify/) that handles various sparsity priors, including our recent average sparsity approach SARA. We evaluate the performance of different priors through simulations in the continuous visibility setting, confirming the superiority of SARA

Introduction to Quantum Information Processing

As a result of the capabilities of quantum information, the science of quantum information processing is now a prospering, interdisciplinary field focused on better understanding the possibilities and limitations of the underlying theory, on developing new applications of quantum information and on physically realizing controllable quantum devices. The purpose of this primer is to provide an elementary introduction to quantum information processing, and then to briefly explain how we hope to exploit the advantages of quantum information. These two sections can be read independently. For reference, we have included a glossary of the main terms of quantum information.Comment: 48 pages, to appear in LA Science. Hyperlinked PDF at http://www.c3.lanl.gov/~knill/qip/prhtml/prpdf.pdf, HTML at http://www.c3.lanl.gov/~knill/qip/prhtm