Abstract: Real-time programmable graphics hardware has resource constraints that prevent complex shaders from rendering in a single pass. One way to virtualize these resources is to partition shading computations into multiple passes, each of which satisfies the given constraints. Many such partitions exist for a shader, but it is important to find one that renders efficiently. We present Recursive Dominator Split (RDS), a polynomial-time algorithm that uses a cost model to find near-optimal partitions of arbitrarily complex shaders. Using a simulator, we analyze partitions for architectures with different resource constraints and show that RDS performs well on different graphics architectures. We also demonstrate that shader partitions computed by RDS can run efficiently on programmable graphics hardware available today.