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 invited to play the following TV game:
You pay $100 to
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 algorithm that has
made possible the modern world.
Dav
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 sub-problems
into a solution to the original problem
Time
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?
Implemented how and in what language?
How do you compare