  This research explores a novel paradigm for preserving topological
segmentations in existing error-bounded lossy compressors. Today's lossy
compressors rarely consider preserving topologies such as Morse-Smale
complexes, and the discrepancies in topology between original and decompressed
datasets could potentially result in erroneous interpretations or even
incorrect scientific conclusions. In this paper, we focus on preserving
Morse-Smale segmentations in 2D/3D piecewise linear scalar fields, targeting
the precise reconstruction of minimum/maximum labels induced by the integral
line of each vertex. The key is to derive a series of edits during compression
time; the edits are applied to the decompressed data, leading to an accurate
reconstruction of segmentations while keeping the error within the prescribed
error bound. To this end, we developed a workflow to fix extrema and integral
lines alternatively until convergence within finite iterations; we accelerate
each workflow component with shared-memory/GPU parallelism to make the
performance practical for coupling with compressors. We demonstrate use cases
with fluid dynamics, ocean, and cosmology application datasets with a
significant acceleration with an NVIDIA A100 GPU.
