I'll discuss our experience in using randomized methods to sample the vertices of a zonotope, which arose when we were studying fast algorithm to solve low-rank correlation clustering problems. I'll also discuss some experience with a new type of Monte Carlo algorithms that appears to have better empirical convergence properties and better parallalization potential when solving linear systems of equations. This work is based on the following papers: https://arxiv.org/abs/1611.07305 and https://arxiv.org/abs/1608.04361