The Complexity Landscape of Distributed Locally Checkable Problems on Trees (opens in new tab)

Recent research revealed the existence of gaps in the complexity landscape of locally checkable labeling (LCL) problems in the LOCAL model of distributed computing. For example, the deterministic round complexity of any LCL problem on bounded-degree graphs is either $O(\log^\ast n)$ or $\Omega(\log n)$ [Chang, Kopelowitz, and Pettie, FOCS 2016]. The complexity landscape of LCL problems is now quite well-understood, but a few questions remain...