  We give simplify the proofs of the 2 results in Marius Zimand's paper
"Kolmogorov complexity version of Slepian-Wolf coding, proceedings of STOC
2017, p22--32". The first is a universal polynomial time compression algorithm:
on input $\varepsilon > 0$, a number $k$ and a string $x$ it computes in
polynomial time with probability $1-\varepsilon$ a program that outputs $x$ and
has length $k + O(\log^2 (|x|/\varepsilon))$, provided that there exists such a
program of length at most $k$. The second result, is a distributed compression
algorithm, in which several parties each send some string to a common receiver.
Marius Zimand proved a variant of the Slepian-Wolf theorem using Kolmogorov
complexity (in stead of Shannon entropy).
  With our simpler proof we improve the parameters of Zimand's result.
