Notes on Better Master Theorems for Divide-and-Conquer Recurrences

Techniques for solving divide-and-conquer recurrences are routinely taught to thousands of Computer Science students each year. The dominant approach to solving such recurrences is known as the Master Method [2]. Recently, Akra and Bazzi [1] discovered a surprisingly elegant generalization of the Master Method that yields a very simple formula for solving most divideand-conquer recurrences. In these notes, we provide a simple inductive proof of the Akra-Bazzi result and we extend the result to handle variations of divide-and-conquer recurrences that commonly arise in practice.