(After about 15 million samples and 7 hours)
The code for the progressive photon mapping is finally written. For the same number of samples, the algorithm does look better than path tracing, but the sample speed is far worse. While I am not quite doing it in the same way as the paper describes, my method has the same, if not better big-O time per sample. A proof has yet to be done for that. Right off the bat I can think of a couple of optimizations: the first two nodes on the photon can be ignored and not added to the map, and the direct lighting can be computed explicitly. I say this because it seems as though this algorithm is much slower for direct lighting, where graininess and complex lighting is not a problem, and fails completely for antialiasing, which is only really important under direct lighting.