Sublinear-round maximal matching and maximal independent set

Determine whether maximal matching or maximal independent set can be computed in o(Delta) rounds in the quantum-LOCAL model for graphs of maximum degree Delta.

Background

The paper derives O(Delta)-round quantum-LOCAL algorithms for maximal matching and maximal independent set in graphs of maximum degree Delta. It records that the only known lower bound is Omega(log Delta / log log Delta), leaving open whether either problem admits a genuinely sublinear dependence on the maximum degree.

References

Can we find a maximal matching or a maximal independent set in $o(\Delta)$ rounds in quantum-LOCAL? The only lower bound is $\Omega(\log \Delta / \log \log \Delta)$ from .

— Quantum Advantage for Distributed Symmetry Breaking  (2609.26788 - Flin et al., 22 Sep 2026) in Section "Open Questions", second problem statement