  We present two fast algorithms which apply inclusion-exclusion principle to
sum over the bosonic diagrams in bare diagrammatic quantum Monte Carlo (dQMC)
and inchworm Monte Carlo method, respectively. In the case of inchworm Monte
Carlo, the proposed fast algorithm gives an extension to the work
["Inclusion-exclusion principle for many-body diagrammatics", Phys. Rev. B,
98:115152, 2018] from fermionic to bosonic systems. We prove that the proposed
fast algorithms reduce the computational complexity from double factorial to
exponential. Numerical experiments are carried out to verify the theoretical
results and to compare the efficiency of the methods.
