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Characterize the trade-off between limited flow splittability and achievable congestion in Clos networks

Characterize the quantitative trade-off between the number of paths allowed per flow (partial splittability) and the minimum achievable congestion for routing in Clos networks; develop bounds and algorithms that relate per-flow path multiplicity constraints to congestion guarantees.

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Background

The paper focuses on unsplittable flows, motivated by practical constraints in current data centers. It suggests that future systems might support splitting each flow over a limited number of paths and highlights the importance of understanding how such partial splittability affects achievable congestion.

This prompts the open problem of formally relating the degree of per-flow path splitting to congestion, including deriving tight bounds and designing algorithms under limited path multiplicity constraints.

References

Our work leaves several open questions. Moving beyond unsplittable flows, it is plausive that future data-centers deploy transport protocols that implement some degree of flow splittability. In this context, it is important to understand the trade-off between the number of paths over which each flow can be split and the minimum congestion achievable.

— Minimum Congestion Routing of Unsplittable Flows in Data-Center Networks (2505.03908 - Ferreira et al., 6 May 2025) in Section 7: Discussion and Open Questions