Think Complexity

Chapter 3. Analysis of Algorithms

Analysis of algorithms is the branch of computer science that studies the performance of algorithms, especially their runtime and space requirements. For more information, see http://en.wikipedia.org/wiki/Analysis_of_algorithms.

The practical goal of algorithm analysis is to predict the performance of different algorithms in order to guide design decisions.

During the 2008 United States presidential campaign, candidate Barack Obama was asked to perform an impromptu analysis when he visited Google. Chief executive Eric Schmidt jokingly asked him for “the most efficient way to sort a million 32-bit integers.” Obama had apparently been tipped off, because he quickly replied, “I think the bubble sort would be the wrong way to go.” See http://www.youtube.com/watch?v=k4RRi_ntQc8.

This is true: bubble sort is conceptually simple but slow for large datasets. The answer Schmidt was probably looking for is “radix sort” (see http://en.wikipedia.org/wiki/Radix_sort).^[4]

The goal of algorithm analysis is to make meaningful comparisons between algorithms, but there are some problems:

• The relative performance of the algorithms might depend on characteristics of the hardware, so one algorithm might be faster on Machine A, another on Machine B. The general solution to this problem is to specify a machine model and analyze the number of steps (or operations) an algorithm requires under a given model.

• Relative performance might depend on the details of the dataset. For ...