The landscape of the distributed time complexity is nowadays well-understood for subpolynomial complexities. When we look at deterministic algorithms in the model and locally checkable problems (s) in bounded-degree graphs, the following picture emerges:

• There are lots of problems with time complexities of or .
• It is not possible to have a problem with complexity between and .
• In general graphs, we can construct problems with infinitely many complexities between and .
• In trees, problems with such complexities do not exist.

However, the high end of the complexity spectrum was left open by prior work. In general graphs there are problems with complexities of the form for any rational , while for trees only complexities of the form are known. No problem with complexity between and o(n) is known, and neither are there results that would show that such problems do not exist. We show that:

• In general graphs, we can construct problems with infinitely many complexities between and o(n).
• In trees, problems with such complexities do not exist.

Put otherwise, we show that any with a complexity o(n) can be solved in time in trees, while the same is not true in general graphs.