Jonathan W. Berry

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.

Tolerating the community detection resolution limit with edge weighting.

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 Barthélemy have proved that modularity maximization algorithms for community detection may fail to resolve communities with fewer than √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 Barthélemys 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 less than √Wε/2 total edge weight, where W is the total edge weight in the network and ε is the maximum weight of an intercommunity edge. If ε 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 ε, we modify the Clauset, Newman, and Moore (CNM) community detection algorithm to maximize weighted modularity, and we 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.

Software and Algorithms for Graph Queries on Multithreaded Architectures

Search-based graph queries, such as finding short paths and isomorphic subgraphs, are dominated by memory latency. If input graphs can be partitioned appropriately, large cluster-based computing platforms can run these queries. However, the lack of compute-bound processing at each vertex of the input graph and the constant need to retrieve neighbors implies low processor utilization. Furthermore, graph classes such as scale-free social networks lack the locality to make partitioning clearly effective. Massive multithreading is an alternative architectural paradigm, in which a large shared memory is combined with processors that have extra hardware to support many thread contexts. The processor speed is typically slower than normal, and there is no data cache. Rather than mitigating memory latency, multithreaded machines tolerate it. This paradigm is well aligned with the problem of graph search, as the high ratio of memory requests to computation can be tolerated via multithreading. In this paper, we introduce the multithreaded graph library (MTGL), generic graph query software for processing semantic graphs on multithreaded computers. This library currently runs on serial machines and the Cray MTA-2, but Sandia is developing a run-time system that will make it possible to run MTGL-based code on symmetric multiprocessors. We also introduce a multithreaded algorithm for connected components and a new heuristic for inexact subgraph isomorphism We explore the performance of these and other basic graph algorithms on large scale-free graphs. We conclude with a performance comparison between the Cray MTA-2 and Blue Gene/Light for s-t connectivity.

Standards for graph algorithm primitives

It is our view that the state of the art in constructing a large collection of graph algorithms in terms of linear algebraic operations is mature enough to support the emergence of a standard set of primitive building blocks. This paper is a position paper defining the problem and announcing our intention to launch an open effort to define this standard.

Advanced Shortest Paths Algorithms on a Massively-Multithreaded Architecture

We present a study of multithreaded implementations of Thorups algorithm for solving the single source shortest path (SSSP) problem for undirected graphs. Our implementations leverage the fledgling multithreaded graph library (MTGL) to perform operations such as finding connected components and extracting induced subgraphs. To achieve good parallel performance from this algorithm, we deviate from several theoretically optimal algorithmic steps. In this paper, we present simplifications that perform better in practice, and we describe details of the multithreaded implementation that were necessary for scalability. We study synthetic graphs that model unstructured networks, such as social networks and economic transaction networks. Most of the recent progress in shortest path algorithms relies on structure that these networks do not have. In this work, we take a step back and explore the synergy between an elegant theoretical algorithm and an elegant computer architecture. Finally, we conclude with a prediction that this work will become relevant to shortest path computation on structured networks.

Realizing parallelism in database operations: insights from a massively multithreaded architecture

A new trend in processor design is increased on-chip support for multithreading in the form of both chip multiprocessors and simultaneous multithreading. Recent research in database systems has begun to explore increased thread-level parallelism made possible by these new multicore and multithreaded processors. The question of how best to use this new technology remains open, particularly as the number of cores per chip and threads per core increase. In this paper we use an existing massively multithreaded architecture, the Cray MTA-2, to explore the implications that a larger degree of on-chip multithreading may have for parallelism in database operations. We find that parallelism in database operations is easy to achieve on the MTA-2 and that, with little effort, parallelism can be made to scale linearly with the number of available processor cores.

Implementing a portable Multi-threaded Graph Library: The MTGL on Qthreads

Developing multi-threaded graph algorithms, even when using the MTGL infrastructure, provides a number of challenges, including discovering appropriate levels of parallelism, preventing memory hot spotting, and eliminating accidental synchronization. In this paper, we have demonstrated that using the combination of Qthreads and MTGL with commodity processors enables the development and testing of algorithms without the expense and complexity of a Cray XMT. While achievable performance is lower for both the Opteron and Niagara platform, performance issues are similar. While we believe it is possible to port Qthreads to the Cray XMT, this work is still on-going. Therefore, porting work still must be done to move algorithm implementations between commodity processors and the XMT. Although it is likely that the Qthreads-version of an algorithm will not be as optimized as a natively implemented version of the algorithm, such a performance impact may be an acceptable trade-off for ease of implementation.

Graph Analysis with High-Performance Computing

Large, complex graphs arise in many settings including the Internet, social networks, and communication networks. To study such data sets, the authors explored the use of high-performance computing (HPC) for graph algorithms. They found that the challenges in these applications are quite different from those arising in traditional HPC applications and that massively multithreaded machines are well suited for graph problems.

US Environmental Protection Agency Uses Operations Research to Reduce Contamination Risks in Drinking Water

The US Environmental Protection Agency (EPA) is the lead federal agency for the security of drinking water in the United States. The agency is responsible for providing information and technical assistance to the more than 50,000 water utilities across the country. The distributed physical layout of drinking-water utilities makes them inherently vulnerable to contamination incidents caused by terrorists. To counter this threat, the EPA is using operations research to design, test, and deploy contamination warning systems (CWSs) that rapidly detect the presence of contaminants in drinking water. We developed a software tool to optimize the design process, published a decision-making process to assist utilities in applying the tool, pilot-tested the tool on nine large water utilities, and provided training and technical assistance to a larger group of utilities. We formed a collaborative team of industry, academia, and government to critique our approach and share CWS deployment experiences. Our work has demonstrated that a CWS is a cost-effective, timely, and capable method of detecting a broad range of contaminants. Widespread application of these new systems will significantly reduce the risks associated with catastrophic contamination incidents: the median estimated fatalities reduction for the nine utilities already studied is 48 percent; the corresponding economic-impact reduction is over

Water Quality Sensor Placement in Water Networks with Budget Constraints

19 billion. Because of this operations research program, online monitoring programs, such as a CWS, are now the accepted technology for reducing contamination risks in drinking water.