Yes, it uses either chordal coloring (written by sebastian hack, who published one of the earlier mentioned graph coloring on SSA papers) or PBQP.
I'm pretty sure LLVM's PBQP implementation is more advanced.
I'm pretty sure LLVM's PBQP implementation is more advanced.
The LLVM implementation is more mature from a software point of view, but libFirm's implementation supports more PBQP reductions, and thus may find a better PBQP solution.