Publications

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.

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.

Phycisal Review Letters

Laviolette, Randall A.; Hendrickson, Bruce A.; Leung, Vitus J.; Phillips, Cynthia A.

Abstract not provided.