Bruce Hendrickson

A Multi-Level Algorithm For Partitioning Graphs

The graph partitioning problem is that of dividing the vertices of a graph into sets of specified sizes such that few edges cross between sets. This NP-complete problem arises in many important scientific and engineering problems. Prominent examples include the decomposition of data structures for parallel computation, the placement of circuit elements and the ordering of sparse matrix computations. We present a multilevel algorithm for graph partitioning in which the graph is approximated by a sequence of increasingly smaller graphs. The smallest graph is then partitioned using a spectral method, and this partition is propagated back through the hierarchy of graphs. A variant of the Kernighan-Lin algorithm is applied periodically to refine the partition. The entire algorithm can be implemented to execute in time proportional to the size of the original graph. Experiments indicate that, relative to other advanced methods, the multilevel algorithm produces high quality partitions at low cost.

An improved spectral graph partitioning algorithm for mapping parallel computations

Efficient use of a distributed memory parallel computer requires that the computational load be balanced across processors in a way that minimizes interprocessor communication. A new domain mapping algorithm is presented that extends recent work in which ideas from spectral graph theory have been applied to this problem. The generalization of spectral graph bisection involves a novel use of multiple eigenvectors to allow for division of a computation into four or eight parts at each stage of a recursive decomposition. The resulting method is suitable for scientific computations like irregular finite elements or differences performed on hypercube or mesh architecture machines. Experimental results confirm that the new method provides better decompositions arrived at more economically and robustly than with previous spectral methods. This algorithm allows for arbitrary nonnegative weights on both vertices and edges to model inhomogeneous computation and communication. A new spectral lower bound for graph bi...

Graph partitioning models for parallel computing

Calculations can naturally be described as graphs in which vertices represent computation and edges reflect data dependencies. By partitioning the vertices of a graph, the calculation can be divided among processors of a parallel computer. However, the standard methodology for graph partitioning minimizes the wrong metric and lacks expressibility. We survey several recently proposed alternatives and discuss their relative merits.

CHALLENGES IN PARALLEL GRAPH PROCESSING

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.

Zoltan data management services for parallel dynamic applications

The Zoltan library is a collection of data management services for parallel, unstructured, adaptive, and dynamic applications that is available as open-source software. It simplifies the load-balancing, data movement, unstructured-communication, and memory usage difficulties that arise in dynamic applications such as adaptive finite-element methods, particle methods, and crash simulations. Zoltans data-structure-neutral design also lets a wide range of applications use it without imposing restrictions on application data structures. Its object-based interface provides a simple and inexpensive way for application developers to use the library and researchers to make new capabilities available under a common interface.The Zoltan library is a collection of data management services for parallel, unstructured, adaptive, and dynamic applications that is available as open-source software from www.cs.sandia.gov/zoltan...

A Scalable Distributed Parallel Breadth-First Search Algorithm on BlueGene/L

Many emerging large-scale data science applications require searching large graphs distributed across multiple memories and processors. This paper presents a distributed breadth- first search (BFS) scheme that scales for random graphs with up to three billion vertices and 30 billion edges. Scalability was tested on IBM BlueGene/L with 32,768 nodes at the Lawrence Livermore National Laboratory. Scalability was obtained through a series of optimizations, in particular, those that ensure scalable use of memory. We use 2D (edge) partitioning of the graph instead of conventional 1D (vertex) partitioning to reduce communication overhead. For Poisson random graphs, we show that the expected size of the messages is scalable for both 2D and 1D partitionings. Finally, we have developed efficient collective communication functions for the 3D torus architecture of BlueGene/L that also take advantage of the structure in the problem. The performance and characteristics of the algorithm are measured and reported.

A Spectral Algorithm for Seriation and the Consecutive Ones Problem

In applications ranging from DNA sequencing through archeological dating to sparse matrix reordering, a recurrent problem is the sequencing of elements in such a way that highly correlated pairs of elements are near each other. That is, given a correlation function f reflecting the desire for each pair of elements to be near each other, find all permutations

Dynamic load balancing in computational mechanics

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Knowledge Mining With VxInsight: Discovery ThroughInteraction

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A New Parallel Method for Molecular Dynamics Simulation of Macromolecular Systems

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