The scheduling of sparse matrix-vector multiplication on a massively parallel dap computer

An efficient data structure is presented which supports general unstructured sparse matrix-vector multiplications on a Distributed Array of Processors (DAP). This approach seeks to reduce the inter-processor data movements and organises the operations in batches of massively parallel steps by a heuristic scheduling procedure performed on the host computer. The resulting data structure is of particular relevance to iterative schemes for solving linear systems. Performance results for matrices taken from well known Linear Programming (LP) test problems are presented and analysed

Chemical structure matching using correlation matrix memories

This paper describes the application of the Relaxation By Elimination (RBE) method to matching the 3D structure of molecules in chemical databases within the frame work of binary correlation matrix memories. The paper illustrates that, when combined with distributed representations, the method maps well onto these networks, allowing high performance implementation in parallel systems. It outlines the motivation, the neural architecture, the RBE method and presents some results of matching small molecules against a database of 100,000 models

An optimized TOPS+ comparison method for enhanced TOPS models

This article has been made available through the Brunel Open Access Publishing Fund.Background Although methods based on highly abstract descriptions of protein structures, such as VAST and TOPS, can perform very fast protein structure comparison, the results can lack a high degree of biological significance. Previously we have discussed the basic mechanisms of our novel method for structure comparison based on our TOPS+ model (Topological descriptions of Protein Structures Enhanced with Ligand Information). In this paper we show how these results can be significantly improved using parameter optimization, and we call the resulting optimised TOPS+ method as advanced TOPS+ comparison method i.e. advTOPS+. Results We have developed a TOPS+ string model as an improvement to the TOPS [1-3] graph model by considering loops as secondary structure elements (SSEs) in addition to helices and strands, representing ligands as first class objects, and describing interactions between SSEs, and SSEs and ligands, by incoming and outgoing arcs, annotating SSEs with the interaction direction and type. Benchmarking results of an all-against-all pairwise comparison using a large dataset of 2,620 non-redundant structures from the PDB40 dataset [4] demonstrate the biological significance, in terms of SCOP classification at the superfamily level, of our TOPS+ comparison method. Conclusions Our advanced TOPS+ comparison shows better performance on the PDB40 dataset [4] compared to our basic TOPS+ method, giving 90 percent accuracy for SCOP alpha+beta; a 6 percent increase in accuracy compared to the TOPS and basic TOPS+ methods. It also outperforms the TOPS, basic TOPS+ and SSAP comparison methods on the Chew-Kedem dataset [5], achieving 98 percent accuracy. Software Availability: The TOPS+ comparison server is available at http://balabio.dcs.gla.ac.uk/mallika/WebTOPS/.This article is available through the Brunel Open Access Publishing Fun

NC Algorithms for Computing a Perfect Matching and a Maximum Flow in One-Crossing-Minor-Free Graphs

In 1988, Vazirani gave an NC algorithm for computing the number of perfect matchings in $K_{3,3}$-minor-free graphs by building on Kasteleyn's scheme for planar graphs, and stated that this "opens up the possibility of obtaining an NC algorithm for finding a perfect matching in $K_{3,3}$-free graphs." In this paper, we finally settle this 30-year-old open problem. Building on recent NC algorithms for planar and bounded-genus perfect matching by Anari and Vazirani and later by Sankowski, we obtain NC algorithms for perfect matching in any minor-closed graph family that forbids a one-crossing graph. This family includes several well-studied graph families including the $K_{3,3}$-minor-free graphs and $K_5$-minor-free graphs. Graphs in these families not only have unbounded genus, but can have genus as high as $O(n)$. Our method applies as well to several other problems related to perfect matching. In particular, we obtain NC algorithms for the following problems in any family of graphs (or networks) with a one-crossing forbidden minor: $\bullet$ Determining whether a given graph has a perfect matching and if so, finding one. $\bullet$ Finding a minimum weight perfect matching in the graph, assuming that the edge weights are polynomially bounded. $\bullet$ Finding a maximum $st$-flow in the network, with arbitrary capacities. The main new idea enabling our results is the definition and use of matching-mimicking networks, small replacement networks that behave the same, with respect to matching problems involving a fixed set of terminals, as the larger network they replace.Comment: 21 pages, 6 figure