  Distributed compression is the task of compressing correlated data by several
parties, each one possessing one piece of data and acting separately. The
classical Slepian-Wolf theorem (D. Slepian, J. K. Wolf, IEEE Transactions on
Inf. Theory, 1973) shows that if data is generated by independent draws from a
joint distribution, that is by a memoryless stochastic process, then
distributed compression can achieve the same compression rates as centralized
compression when the parties act together. Recently, the author (M. Zimand,
STOC 2017) has obtained an analogue version of the Slepian-Wolf theorem in the
framework of Algorithmic Information Theory (also known as Kolmogorov
complexity). The advantage over the classical theorem, is that the AIT version
works for individual strings, without any assumption regarding the generative
process. The only requirement is that the parties know the complexity profile
of the input strings, which is a simple quantitative measure of the data
correlation. The goal of this paper is to present in an accessible form that
omits some technical details the main ideas from the reference (M. Zimand, STOC
2017).
