The sublinear running-time dichotomy conjecture

Let $H$ be a connected infection rule, and let $M_H(n)$ denote its maximum running time. Sublinear dichotomy conjecture. If

$$M_H(n)=o(n),$$

then

$$M_H(n)=\Theta(1)\quad\text{or}\quad M_H(n)=\Theta(\log n).$$

The paper describes the classification of connected infection rules with sublinear maximum running time as open. The conjecture predicts that no other asymptotic growth rates occur in the sublinear regime.