Finding a minimum spanning tree (MST) for $n$ points in an arbitrary metric space is a fundamental primitive for hierarchical clustering and many other ML tasks, but this takes $\Omega(n^2)$ time to even approximate. We introduce a framework for metric MSTs that first (1) finds a forest of trees using practical heuristics, and then (2) finds a small weight set of edges to connect disjoint components in the forest into a spanning tree. We prove that optimally solving step (2) still takes $\Omega(n^2)$ time, but we provide a subquadratic 2.62-approximation algorithm. In the spirit of learning-augmented algorithms, we then show that if the heuristic forest found in step (1) overlaps with an optimal MST, we can approximate the original MST problem in subquadratic time, where the approximation factor depends on a measure of overlap. In practice, we find nearly optimal spanning trees for a wide range of metrics, while being orders of magnitude faster than exact algorithms.

YGM is a general-purpose asynchronous distributed computing library for C++/MPI, designed to handle the irregular data access patterns and small messages of graph algorithms and data science applications. It uses data serialization to give an easily usable active message interface and message aggregation to maximize application throughput. Our design philosophy makes a tradeoff that increases network bandwidth utilization at the cost of added latency. We provide a suite of benchmarks showcasing YGM's performance. Compared to similar distributed active message benchmark implementations that do not provide message buffering, we are able to achieve over 10x throughput on thousands of cores at a latency cost that can be as small as 2x or as large as 100x, depending on the machine being used. For applications that can be written to be latency-tolerant, this represents a significant potential performance improvement through using YGM.

Understanding the higher-order interactions within network data is a key objective of network science. Surveys of metadata triangles (or patterned 3-cycles in metadata-enriched graphs) are often of interest in this pursuit. In this work, we develop TriPoll, a prototype distributed HPC system capable of surveying triangles in massive graphs containing metadata on their edges and vertices. We contrast our approach with much of the prior effort on triangle analysis, which often focuses on simple triangle counting, usually in simple graphs with no metadata. We assess the scalability of TriPoll when surveying triangles involving metadata on real and synthetic graphs with up to hundreds of billions of edges. We utilize communication-reducing optimizations to demonstrate a triangle counting task on a 224 billion edge web graph in approximately half of the time of competing approaches, while additionally supporting metadata-aware capabilities.