Approximation guarantee under restricted replica sets

Establish an additive approximation guarantee for expert-parallel fixed-charge makespan dispatch when each expert is replicated only on a restricted subset of GPUs, extending the full-replication guarantee proved for the round-robin construction.

Background

The paper proves an additive guarantee for a descending-token round-robin placement under full replication, where every expert can be assigned to every GPU. Under restricted replica sets, that construction may be infeasible, and the proof’s row-domination argument no longer applies directly.

An additive guarantee in the restricted-replication setting would provide a principled performance certificate for the practically relevant case in which placement constraints determine which GPUs can host each expert. The appendix reports an empirical conjecture involving a “fewest-experts replica, token tie-break” rule, but no theorem is established.

References

With restricted replicas $A_3$ is generally infeasible and we have no analogous guarantee (open problem, \cref{sec:limits}).

— TEMPO: Makespan-Aware Expert-Parallel Load Balancing Across Memory- and Compute-Bound Regimes  (2608.13057 - Li et al., 13 Aug 2026) in Section 3, subsection “Fixed-charge makespan dispatch,” immediately after Theorem 3.3; discussed again in Appendix, Remark “restricted replication”