  The Stochastic Green Function (SGF) algorithm is able to simulate any
Hamiltonian that does not suffer from the so-called "sign problem". We propose
a new global space-time update scheme for the SGF algorithm which, in addition
to being simpler than the previous formulation, reduces auto-correlation times.
Using as a concrete example the extended Bose-Hubbard model and the complex
Hamiltonian with six-site ring-exchange interactions which was recently studied
in ArXiv:1206.2566v1, we present a comprehensive review of the SGF algorithm
and the new updating scheme. Measurements of non-trivial physical quantities
are presented in detail. While the SGF algorithm works in the canonical
ensemble by nature, we give a simple extension that allows us to perform
simulations in the grand-canonical ensemble too. We also discuss an optimized
implementation which allows for access to large system sizes.
