Processor allocation strategies for modified hypercubes

Parallel processing has been widely accepted to be the future in high speed computing. Among the various parallel architectures proposed/implemented, the hypercube has shown a lot of promise because of its poweful properties, like regular topology, fault tolerance, low diameter, simple routing, and ability to efficiently emulate other architectures. The major drawback of the hypercube network is that it can not be expanded in practice because the number of communication ports for each processor grows as the logarithm of the total number of processors in the system. Therefore, once a hypercube supercomputer of a certain dimensionality has been built, any future expansions can be accomplished only by replacing the VLSI chips. This is an undesirable feature and a lot of work has been under progress to eliminate this stymie, thus providing a platform for easier expansion. Modified hypercubes (MHs) have been proposed as the building blocks of hypercube-based systems supporting incremental growth techniques without introducing extra resources for individual hypercubes. However, processor allocation on MHs proves to be a challenge due to a slight deviation in their topology from that of the standard hypercube network. This thesis addresses the issue of processor allocation on MHs and proposes various strategies which are based, partially or entirely, on table look-up approaches. A study of the various task allocation strategies for standard hypercubes is conducted and their suitability for MHs is evaluated. It is shown that the proposed strategies have a perfect subcube recognition ability and a superior performance. Existing processor allocation strategies for pure hypercube networks are demonstrated to be ineffective for MHs, in the light of their inability to recognize all available subcubes. A comparative analysis that involves the buddy strategy and the new strategies is carried out using simulation results

A bibliography on parallel and vector numerical algorithms

This is a bibliography of numerical methods. It also includes a number of other references on machine architecture, programming language, and other topics of interest to scientific computing. Certain conference proceedings and anthologies which have been published in book form are listed also

Optimal cube-connected cube multiprocessors

Many CFD (computational fluid dynamics) and other scientific applications can be partitioned into subproblems. However, in general the partitioned subproblems are very large. They demand high performance computing power themselves, and the solutions of the subproblems have to be combined at each time step. The cube-connect cube (CCCube) architecture is studied. The CCCube architecture is an extended hypercube structure with each node represented as a cube. It requires fewer physical links between nodes than the hypercube, and provides the same communication support as the hypercube does on many applications. The reduced physical links can be used to enhance the bandwidth of the remaining links and, therefore, enhance the overall performance. The concept and the method to obtain optimal CCCubes, which are the CCCubes with a minimum number of links under a given total number of nodes, are proposed. The superiority of optimal CCCubes over standard hypercubes was also shown in terms of the link usage in the embedding of a binomial tree. A useful computation structure based on a semi-binomial tree for divide-and-conquer type of parallel algorithms was identified. It was shown that this structure can be implemented in optimal CCCubes without performance degradation compared with regular hypercubes. The result presented should provide a useful approach to design of scientific parallel computers

On the performance of a cavity method based algorithm for the Prize-Collecting Steiner Tree Problem on graphs

We study the behavior of an algorithm derived from the cavity method for the Prize-Collecting Steiner Tree (PCST) problem on graphs. The algorithm is based on the zero temperature limit of the cavity equations and as such is formally simple (a fixed point equation resolved by iteration) and distributed (parallelizable). We provide a detailed comparison with state-of-the-art algorithms on a wide range of existing benchmarks networks and random graphs. Specifically, we consider an enhanced derivative of the Goemans-Williamson heuristics and the DHEA solver, a Branch and Cut Linear/Integer Programming based approach. The comparison shows that the cavity algorithm outperforms the two algorithms in most large instances both in running time and quality of the solution. Finally we prove a few optimality properties of the solutions provided by our algorithm, including optimality under the two post-processing procedures defined in the Goemans-Williamson derivative and global optimality in some limit cases

Spatial gradient consistency for unsupervised learning of hyperspectral demosaicking: Application to surgical imaging

Hyperspectral imaging has the potential to improve intraoperative decision making if tissue characterisation is performed in real-time and with high-resolution. Hyperspectral snapshot mosaic sensors offer a promising approach due to their fast acquisition speed and compact size. However, a demosaicking algorithm is required to fully recover the spatial and spectral information of the snapshot images. Most state-of-the-art demosaicking algorithms require ground-truth training data with paired snapshot and high-resolution hyperspectral images, but such imagery pairs with the exact same scene are physically impossible to acquire in intraoperative settings. In this work, we present a fully unsupervised hyperspectral image demosaicking algorithm which only requires exemplar snapshot images for training purposes. We regard hyperspectral demosaicking as an ill-posed linear inverse problem which we solve using a deep neural network. We take advantage of the spectral correlation occurring in natural scenes to design a novel inter spectral band regularisation term based on spatial gradient consistency. By combining our proposed term with standard regularisation techniques and exploiting a standard data fidelity term, we obtain an unsupervised loss function for training deep neural networks, which allows us to achieve real-time hyperspectral image demosaicking. Quantitative results on hyperspetral image datasets show that our unsupervised demosaicking approach can achieve similar performance to its supervised counter-part, and significantly outperform linear demosaicking. A qualitative user study on real snapshot hyperspectral surgical images confirms the results from the quantitative analysis. Our results suggest that the proposed unsupervised algorithm can achieve promising hyperspectral demosaicking in real-time thus advancing the suitability of the modality for intraoperative use

Adapting the interior point method for the solution of linear programs on high performance computers

In this paper we describe a unified algorithmic framework for the interior point method (IPM) of solving Linear Programs (LPs) which allows us to adapt it over a range of high performance computer architectures. We set out the reasons as to why IPM makes better use of high performance computer architecture than the sparse simplex method. In the inner iteration of the IPM a search direction is computed using Newton or higher order methods. Computationally this involves solving a sparse symmetric positive definite (SSPD) system of equations. The choice of direct and indirect methods for the solution of this system and the design of data structures to take advantage of coarse grain parallel and massively parallel computer architectures are considered in detail. Finally, we present experimental results of solving NETLIB test problems on examples of these architectures and put forward arguments as to why integration of the system within sparse simplex is beneficial

ALGORITMA ROUTING UNTUK IDENTIFIKASI JALURTERPENDEK PADA INCOMPLETE-HYPERCUBE_UG

Pada tulisan ini dibahas tentang pengembangan suatu algoritma routing untuk menentukan jalur terpendek antara dua prosesor di dalam hypercube yang faulty (incomplete hypercube). Algoritma ini dapat mengidentifikasi kondisi konektifiti jaringan ketika beberapa prosesor pada jalur menjadi faulty. Pada saat kondisi jaringan tetap tehubung, algoritma selalu dapat menunjukkan panjang jalur terpendek antara dua prosesor. Konsep jarak Hamming dan graf kombinatorik himpunan string biner digunakan dalam mendisain Algoritma. Kompleksitas algoritma ini adalah O(N), N adalah jumlah simpul dalam incomplete-hypercube