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Complexity of the Order Degree Problem (ODP)

Prove NP-hardness or polynomial-time solvability of the Order Degree Problem—given n and a maximum degree d, minimize the diameter—and provide a formal complexity classification (including any parameterized or approximation status).

References

In this work, we consider the ODP, for which--to our knowledge--an NP-hardness proof is not available in the open literature.

— Quantum Optimization Benchmark Library -- The Intractable Decathlon (Koch et al., 4 Apr 2025) in Section 4.10 (Topology Design), Background