Implementations of Broadcast based on some information dissemination algorithm -- e.g., gossip or tree-based communication -- followed by a correction algorithm has been proposed previously. This work describes an approach to apply a similar idea to Reduce. In it, a correction-like communication phase precedes a tree-based phase. This provides a Reduce algorithm which is tolerant to a number of failed processes. Semantics of the resulting algorithm are provided and proven. Based on these results, Broadcast and Reduce are combined to provide Allreduce.
@article{arxiv.2602.22445,
title = {Fault-tolerant Reduce and Allreduce operations based on correction},
author = {Martin Kuettler and Hermann Haertig},
journal= {arXiv preprint arXiv:2602.22445},
year = {2026}
}