10 most influential algorithms

Through the twitter feed of Tim O’Reilly, I came across this great post on network flow algorithms. Not only did I have fun revisiting the Min Cut / Max Flow, but there was a great link to an article listing the “10 algorithms with the greatest influence on the development and practice of science and engineering in the 20th century”. I am very excited, as for a few of them, I have absolutely no idea what they are about; it has always fascinated me to see the isolation of research fields, and how much they don’t know about each other.

Here is the official list:

Metropolis Algorithm for Monte Carlo
Simplex Method for Linear Programming
Krylov Subspace Iteration Methods
The Decompositional Approach to Matrix Computations
The Fortran Optimizing Compiler
QR Algorithm for Computing Eigenvalues
Quicksort Algorithm for Sorting
Fast Fourier Transform
Integer Relation Detection
Fast Multipole Method

Which ones do you know? And how did you come across them?