  The computation of determinants plays a central role in diagrammatic Monte
Carlo algorithms for strongly correlated systems. The evaluation of large
numbers of determinants can often be the limiting computational factor
determining the number of attainable diagrammatic expansion orders. In this
work we build upon the algorithm presented in [\emph{Linear Algebra and its
applications} 419.1 (2006), 107-124] which computes all principal minors of a
matrix in $O(2^n)$ operations. We present multiple generalizations of the
algorithm to the efficient evaluation of certain subsets of all principal
minors with immediate applications to Connected Determinant Diagrammatic Monte
Carlo within the normal and symmetry-broken phases as well as Continuous-time
Quantum Monte Carlo. Additionally, we improve the asymptotic scaling of
diagrammatic Monte Carlo formulated in real-time to $O(2^n)$ and report
speedups of up to a factor $25$ at computationally realistic expansion orders.
We further show that all permanent-principal-minors, corresponding to sums of
bosonic Feynman diagrams, can be computed in $O(3^n)$, making diagrammatic
Monte Carlo for bosonic and mixed systems a viable path worth exploring.
