Randomized Algorithms
Randomized Algorithms
Chance favors only the prepared mind.
Those unprepared cannot see the hand
stretched out to them by fortune
Louis Pasteur (1822-1895)
1
Motivation
You are
University of Denver
Prof. M. Lopez
Two ideas lie gleaming in the
scientists chest: the first is the
calculus, the second, the
algorithm. The calculus made
modern science possible; but it
has been the
COMP 3371
Divide and Conquer
Given a problem of size n:
1) Divide the problem into k sub-problems of
size n/k each
2) Conquer by solving each sub-problem
independently
3) Combine the k solutions to su
Review: Algorithm Efficiency
A first attempt: an algorithm is efficient if, when
implemented, it runs quickly on real input instances
What is missing?
What does quickly really mean?
Run where?
Im