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We analyze a simple hill-climbing algorithm (RMHC) that was pre (cid: 173) viously shown to outperform a genetic algorithm (GA) on a simple" Royal Road" function. We then analyze an" idealized" genetic algorithm (IGA) that is significantly faster than RMHC and that gives a lower bound for GA speed. We identify the features of the IGA that give rise to this speedup, and discuss how these features can be incorporated into a real GA.