Explore a comprehensive lecture on approximation algorithms in theoretical computer science. Delve into the intricacies of Boolean formula satisfiability, algorithmic complexity theory, and various optimization problems. Learn about Gavril's Approximation Algorithm, Max-Cut, and the Vertex-Cover problem, including examples and analyses of greedy approaches. Discover the 2-approximation theorem for Vertex-Cover and explore the k-Coverage and Pokémon-Coverage problems. Examine the Traveling Salesperson Problem (TSP) with practical examples, and gain insights into its applications in museum exhibit planning and textbook organization.
Great Ideas in Theoretical Computer Science - Approximation Algorithms
Overview
Syllabus
Intro
given a Boolean formula F. is it satisfiable?
INVENTS BEAUTIFUL THEORY OF ALGORITHMIC COMPLEXITY
Don't Give Up
Gavril's Approximation Algorithm
Max-Cut
A technicality: Optimization vs. Decision
Today: A case study of
A possible Vertex-Cover algorithm
GreedyVC example
GreedyVc analysis
A bad graph for GreedyVc
A worse graph for GreedyVc
Greed is Bad (for Vertex-Cover)
Gavril to the rescue
GavrilVC example
Theorem: GavrilVC is a 2-approximation for Vertex-Cover.
"k-Coverage" problem
"Pokémon-Coverage" problem
Example with k=3
Greed is Pretty Good (for k-Coverage)
TSP (Traveling Salesperson Problem)
TSP example
Textbooks
Museum exhibits
Taught by
Ryan O'Donnell
