Admittedly I haven't fully wrapped my head around the paper yet, but I'm curious if this algorithm can be adapted to say, a one dimensional cellular automata with two states, and an even sized neighborhood, there are references in the paper to "neighbor radius" and neighborhood size of 2r+1. But the reversibility of neighborhoods of size 2, 4, and 6, for example, are also of interest to me.
A link to the paper is here: https://wpmedia.wolfram.com/uploads/sites/13/2018/02/05-1-3.pdf
I know of one other algorithm, from Amoroso and Patt (1972) that seems to be generally applicable to even numbered neighborhoods from a brief overview of the paper, but I can't seem to find a time complexity analysis of it within or without. Although, other papers seem to imply it is worse than quadratic. (And I have been less able to understand the paper)