Figure depicts the typical situation of an active space with a similar number of particles and spatial orbitals, hence the constrained subset, for both particle-and hole-selection, contains half of the elements of the total system size. In the same Figure we can see the linear scaling for both methods and that the redrawing method is roughly five times faster than rebuilding the alias sampling tables. For higher weights of the constrained subset, the redrawing method can get up to ten times faster. Further details of the timings are discussed in the Appendix A.1. Redraw from alias sampler and renormalize Rebuild alias sampler for constrained set Figure : Sampling time for drawing from a constrained subsets that contains half of the elements of the total system size using two different algorithms: redrawing method (blue line, algorithm 3) and rebuilding an alias table for the constrained subset (orange line).