So, the REU is nearing its end for me and I have not been reporting
anything here... what's the matter?

The problem is at first I got very excited, to later realize that in
fact I'm stuck.

The past four weeks I was working on a coloring algorithm for
shrub-depth, trying to generalize the very simple and elegant ILP
solution presented by Michael Lampis in the original ND paper. I and
Vojta investigated a few approaches during our time at Princeton. I
decided to pursue one that looked promising, and for some time felt I
solved the problem. However, when I tried writing down the solution, I
found out I've only solved a part of the problem, and the easier one
at that.

Roughly speaking the task is the following. I need to find a
"canonical" way to describe colorings of graphs of bounded shrub-depth
such that this canonical way would be expressible as a solution to an
ILP, but it has to be succinct enough to only need \(f(k,d)\)
variables,
for \(k\)
the number of labels and \(d\)
the shrub-depth. This "canonical
form" approach was successful in my thesis and other ND-related
research, but I know of no examples where it would work for
shrub-depth. We'll have to see. For now I'm in the "stuck" phase,
which just sometimes happens in research. It sucks, but it is necessary.

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