EXaCTz: Guaranteed Extremum Graph and Contour Tree Preservation for Distributed- and GPU-Parallel Lossy Compression

2026-04-01

AI Summary

Existing topology-preserving lossy compression methods suffer from low throughput, limited support for topological descriptors, and a lack of theoretical convergence guarantees. This work proposes a high-performance parallel compression algorithm that jointly preserves the fidelity of extremum graphs and contour trees for the first time, avoiding explicit topological reconstruction by enforcing constraints on vertex extremum neighborhood relations and the global ordering of critical points. Built upon GPU and distributed architectures, the method employs a bounded iterative refinement strategy coupled with vulnerability graph analysis to model cascade effects, yielding provable convergence bounds. Experiments demonstrate a single-GPU correction throughput of 4.52 GB/s—up to 3,285× faster than existing approaches—and achieve sub-48-second processing of 512 GB datasets using 128 GPUs, attaining an aggregate throughput of 32.69 GB/s.

Abstract

This paper introduces EXaCTz, a parallel algorithm that concurrently preserves extremum graphs and contour trees in lossy-compressed scalar field data. While error-bounded lossy compression is essential for large-scale scientific simulations and workflows, existing topology-preserving methods suffer from (1) a significant throughput disparity, where topology correction speeds are on the order of MB/s, lagging orders of magnitude behind compression speeds on the order of GB/s, (2) limited support for diverse topological descriptors, and (3) a lack of theoretical convergence bounds. To address these challenges, EXaCTz introduces a high-performance, bounded-iteration algorithm that enforces topological consistency by deriving targeted edits for decompressed data. Unlike prior methods that rely on explicit topology reconstruction, EXaCTz enforces consistent min/max neighbors of all vertices, along with global ordering among critical points. As such, the algorithm enforces consistent critical-point classification, saddle extremum connectivity, and the preservation of merge/split events. We theoretically prove the convergence of our algorithm, bounded by the longest path in a vulnerability graph that characterizes potential cascading effects during correction. Experiments on real-world datasets show that EXaCTz achieves a single-GPU throughput of up to 4.52 GB/s, outperforming the state-of-the-art contour-tree-preserving method (Gorski et al.) by up to 213x (with a single-core CPU implementation for fair comparison) and 3,285x (with a single-GPU version). In distributed environments, EXaCTz scales to 128 GPUs with 55.6\% efficiency (compared with 6.4\% for a naive parallelization), processing datasets of up to 512 GB in under 48 seconds and achieving an aggregate correction throughput of up to 32.69 GB/s.

Problem

• topology preservation
• lossy compression
• extremum graph
• contour tree
• throughput disparity

Innovation

• topology-preserving compression
• extremum graph
• contour tree
• GPU-parallel algorithm
• convergence guarantee