Author

Francesco d’Amore

Gran Sasso Science Institute

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Preprint Aug 2026

Superlogarithmic Gap Result for LCLs on Trees in Quantum-LOCAL

We show that, on trees, any locally checkable labeling problem (LCL) $\Pi$ that can be solved by an $n^{o(1)}$-dependent distribution can also be solved by an $O(\log n)$-round deterministic LOCAL algorithm. The result is obtained through a rake-and-compress-style decomposition of the input tree, and local simulations...

Francesco d’Amore, Henrik Lievonen · 1 citation