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Advances in Domain Mapping of Massively Parallel Scientific Computations

Leland, Robert; Hendrickson, Bruce A.

One of the most important concerns in parallel computing is the proper distribution of workload across processors. For most scientific applications on massively parallel machines, the best approach to this distribution is to employ data parallelism; that is, to break the datastructures supporting a computation into pieces and then to assign those pieces to different processors. Collectively, these partitioning and assignment tasks comprise the domain mapping problem.

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Parallel Processing Letters

Hendrickson, Bruce A.; Berry, Jonathan W.

Graph algorithms are becoming increasingly important for solving many problems in scientific computing, data mining and other domains. As these problems grow in scale, parallel computing resources are required to meet their computational and memory requirements. Unfortunately, the algorithms, software, and hardware that have worked well for developing mainstream parallel scientific applications are not necessarily effective for large-scale graph problems. In this paper we present the inter-relationships between graph problems, software, and parallel hardware in the current state of the art and discuss how those issues present inherent challenges in solving large-scale graph problems. The range of these challenges suggests a research agenda for the development of scalable high-performance software for graph problems.

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LDRD final report : massive multithreading applied to national infrastructure and informatics

Barrett, Brian B.; Hendrickson, Bruce A.; Laviolette, Randall A.; Leung, Vitus J.; Mackey, Greg; Murphy, Richard C.; Phillips, Cynthia A.; Pinar, Ali P.

Large relational datasets such as national-scale social networks and power grids present different computational challenges than do physical simulations. Sandia's distributed-memory supercomputers are well suited for solving problems concerning the latter, but not the former. The reason is that problems such as pattern recognition and knowledge discovery on large networks are dominated by memory latency and not by computation. Furthermore, most memory requests in these applications are very small, and when the datasets are large, most requests miss the cache. The result is extremely low utilization. We are unlikely to be able to grow out of this problem with conventional architectures. As the power density of microprocessors has approached that of a nuclear reactor in the past two years, we have seen a leveling of Moores Law. Building larger and larger microprocessor-based supercomputers is not a solution for informatics and network infrastructure problems since the additional processors are utilized to only a tiny fraction of their capacity. An alternative solution is to use the paradigm of massive multithreading with a large shared memory. There is only one instance of this paradigm today: the Cray MTA-2. The proposal team has unique experience with and access to this machine. The XMT, which is now being delivered, is a Red Storm machine with up to 8192 multithreaded 'Threadstorm' processors and 128 TB of shared memory. For many years, the XMT will be the only way to address very large graph problems efficiently, and future generations of supercomputers will include multithreaded processors. Roughly 10 MTA processor can process a simple short paths problem in the time taken by the Gordon Bell Prize-nominated distributed memory code on 32,000 processors of Blue Gene/Light. We have developed algorithms and open-source software for the XMT, and have modified that software to run some of these algorithms on other multithreaded platforms such as the Sun Niagara and Opteron multi-core chips.

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Tolerating the community detection resolution limit with edge weighting

Proposed for publication in the Proceedings of the National Academy of Sciences.

Hendrickson, Bruce A.; Laviolette, Randall A.; Phillips, Cynthia A.; Berry, Jonathan W.

Communities of vertices within a giant network such as the World-Wide-Web are likely to be vastly smaller than the network itself. However, Fortunato and Barthelemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than {radical} L/2 edges, where L is the number of edges in the entire network. This resolution limit leads modularity maximization algorithms to have notoriously poor accuracy on many real networks. Fortunato and Barthelemy's argument can be extended to networks with weighted edges as well, and we derive this corollary argument. We conclude that weighted modularity algorithms may fail to resolve communities with fewer than {radical} W{epsilon}/2 total edge weight, where W is the total edge weight in the network and {epsilon} is the maximum weight of an inter-community edge. If {epsilon} is small, then small communities can be resolved. Given a weighted or unweighted network, we describe how to derive new edge weights in order to achieve a low {epsilon}, we modify the 'CNM' community detection algorithm to maximize weighted modularity, and show that the resulting algorithm has greatly improved accuracy. In experiments with an emerging community standard benchmark, we find that our simple CNM variant is competitive with the most accurate community detection methods yet proposed.

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Solving elliptic finite element systems in near-linear time with support preconditioners

SIAM Journal on Numerical Analysis

Boman, Erik G.; Hendrickson, Bruce A.; Vavasis, Stephen

We consider linear systems arising from the use of the finite element method for solving scalar linear elliptic problems. Our main result is that these linear systems, which are symmetric and positive semidefinite, are well approximated by symmetric diagonally dominant matrices. Our framework for defining matrix approximation is support theory. Significant graph theoretic work has already been developed in the support framework for preconditioners in the diagonally dominant case, and, in particular, it is known that such systems can be solved with iterative methods in nearly linear time. Thus, our approximation result implies that these graph theoretic techniques can also solve a class of finite element problems in nearly linear time. We show that the support number bounds, which control the number of iterations in the preconditioned iterative solver, depend on mesh quality measures but not on the problem size or shape of the domain. © 2008 Society for Industrial and Applied Mathematics.

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Results 1–25 of 57
Results 1–25 of 57