Could you explain how shift-PPLNS and shift-DGM work ? I have seen you use that expression before, but I have never seen you explain it. Are you refering to the version of DGM where the logarithms of the scores are used ?  Using 2 as a logarithm base, addition of exponents would be equivalent to binary shifting.

Can you have distributed DGM with per-node worker scores and "s" variable and then add all the nodes together later ?