The goal of this project is to build a register pressure aware instruction scheduler.
Although such schedulers are already used in compilers such as gcc or llvm, none of them is based on a research paper.
Furthermore, all research papers on the subject come up with heuristics.

I think that this approach is not the good one given that for the vast majority of DAGs, finding an optimal scheduler (which minimizes the register pressure) is feasable.
The problem is stil NP-complete is the general case but this no way near a good reason to try random heuristics.

My approach is to take a DAG and to reduce it using various transformation which preserve optimality.
Ultimately the DAG still has to be scheduled and more importantly, the scheduler has to solve an even more complicated problem than at the beginning because I allow each schedule unit to have an internal register pressure and to create several variables.
This is not a problem in practice because the preferred scheduling backend is an ILP solver using a smartly constructed ILP program.
If the DAGs is too big for an ILP to solve it in reasonable time, there is always the possibility to plug a custom scheduler backend.