David A. Bader

James P. Fairbanks, Geoffrey D. Sanders, David A. Bader

Many common methods for data analysis rely on linear algebra. We provide new results connecting data analysis error to numerical accuracy, which leads to the first meaningful stopping criterion for two way spectral partitioning. More generally, we provide pointwise convergence guarantees so that blends (linear combinations) of eigenvectors can be employed to solve data analysis problems with confidence in their accuracy. We demonstrate this theory on an accessible model problem, the Ring of Cliques, by deriving the relevant eigenpairs and comparing the predicted results to numerical solutions. These results bridge the gap between linear algebra based data analysis methods and the convergence theory of iterative approximation methods.

David A. Bader

In the 1980s, high-performance computing (HPC) became another tool for research in the open (non-defense) science and engineering research communities. However, HPC came with a high price tag; the first Cray-2 machines, released in 1985, cost between \$12 million and \$17 million, according to the Computer History Museum, and were largely available only at government research labs or through national supercomputing centers. In the 1990s, with demand for HPC increasing due to vast datasets, more complex modeling, and the growing computational needs of scientific applications, researchers began experimenting with building HPC machines from clusters of servers running the Linux operating system. By the late 1990s, two approaches to Linux-based parallel computing had emerged: the personal computer cluster methodology that became known as Beowulf and the Roadrunner architecture aimed at a more cost-effective supercomputer. While Beowulf attracted attention because of its low cost and thereby greater accessibility, Roadrunner took a different approach. While still affordable compared to vector processors and other commercially available supercomputers, Roadrunner integrated its commodity components with specialized networking technology. Furthermore, these systems initially served different purposes. While Beowulf focused on providing affordable parallel workstations for individual researchers at NASA, Roadrunner set out to provide a multi-user system that could compete with the commercial supercomputers that dominated the market at the time. This paper analyzes the technical decisions, performance implications, and long-term influence of both approaches. Through this analysis, we can start to judge the impact of both Roadrunner and Beowulf on the development of Linux-based supercomputers.

Vikram Ramavarapu, João Alfredo Cardoso Lamy, Mohammad Dindoost et al.

Community detection, or network clustering, is used to identify latent community structure in networks. Due to the scarcity of labeled ground truth in real-world networks, evaluating these algorithms poses significant challenges. To address this, researchers use synthetic network generators that produce networks with ground-truth community labels. RECCS is one such algorithm that takes a network and its clustering as input and generates a synthetic network through a modular pipeline. Each generated ground truth cluster preserves key characteristics of the corresponding input cluster, including connectivity, minimum degree, and degree sequence distribution. The output consists of a synthetically generated network, and disjoint ground truth cluster labels for all nodes. In this paper, we present two enhanced versions: RECCS+ and RECCS++. RECCS+ maintains algorithmic fidelity to the original RECCS while introducing parallelization through an orchestrator that coordinates algorithmic components across multiple processes and employs multithreading. RECCS++ builds upon this foundation with additional algorithmic optimizations to achieve further speedup. Our experimental results demonstrate that RECCS+ and RECCS++ achieve speedups of up to 49x and 139x respectively on our benchmark datasets, with RECCS++'s additional performance gains involving a modest accuracy tradeoff. With this newfound performance, RECCS++ can now scale to networks with over 100 million nodes and nearly 2 billion edges.