Abstract. As register allocation is one of the most important phases in optimizing compilers, much work has been done to improve its quality and speed. We present a novel register allocation architecture for programs in SSA-form which simplifies register allocation significantly. We investigate certain properties of SSA-programs and their interference graphs, showing that they belong to the class of chordal graphs. This leads to a quadratic-time optimal coloring algorithm and allows for decoupling the tasks of coloring, spilling and coalescing completely. After presenting heuristic methods for spilling and coalescing, we compare our coalescing heuristic to an optimal method based on integer linear programming.

This paper gives a constructive proof that the register allocation problem for a uniform register set is solvable in polynomial time for SSA-form programs.

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