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Notes on Better Master Theorems for Divide-and-Conquer Recurrences (1996)
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| Venue: | Lecture notes, MIT |
| Citations: | 6 - 0 self |
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@INPROCEEDINGS{Leighton96noteson,
author = {Tom Leighton},
title = {Notes on Better Master Theorems for Divide-and-Conquer Recurrences},
booktitle = {Lecture notes, MIT},
year = {1996}
}
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Abstract
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. 1 Introduction Divide-and-conquer recurrences are ubiquitous in the analysis of algorithms. Many methods are known for solving recurrences such as T (n) = ( 1 if n = 1 2T (dn=2e) +O(n) if n ? 1; but perhaps the most widely taught approach is the Master Method that is described in the seminal algorithms text by Cormen, Leiserson and Rivest [2]. The Master Method is fairly powerful and results in a closed form s...
Keyphrases
divide-and-conquer recurrence master method better master theorem computer science student dominant approach taught approach akra-bazzi result seminal algorithm text simple inductive proof introduction divide-and-conquer recurrence elegant generalization closed form many method divideand conquer recurrence simple formula
