The investigation of Markov chains is a remarkable research area due to the simplicity of the basic concepts and the wide range of successful applications. A key question is efficiency, which is quantified by the mixing time, through the decrease of total variation distance to stationarity.

A typical setup in Markov chain Monte Carlo problems is that there is an a priori given stationary distribution to be attained and a graph defining the set of feasible moves, then the systematic design of Markov chains satisfying the this structural constraints with low mixing time is an additional challenge.