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Narrow the online 2 vs 3 gap for Clos unsplittable flows

Develop an online algorithm for minimum congestion routing of unsplittable flows in Clos networks with competitive ratio 2, matching the lower bound established for online algorithms, or otherwise prove stronger lower bounds that preclude such an improvement over the current 3-competitive guarantee.

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Background

For online routing, the paper proves that no online algorithm (deterministic or randomized) can achieve approximation better than 2, establishing a lower bound of 2. It also notes that a simple Unsorted Greedy algorithm achieves an upper bound of 3.

This creates a gap between the 2 lower bound and the 3 upper bound, and the open problem is to close this gap—ideally by designing a 2-competitive online algorithm.

References

Our work leaves several open questions. Similarly to the offline setting, in the online setting, the key question is to narrow the gap with respect to congestion and approximation between the 2 factor yielded by the new lower bounds and the 3 factor yielded by the Unsorted Greedy algorithm.

— 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