Will It Ever End?

Classic Results

Review of NP-completeness and Sample Problems

A sample transform: 3-SAT to Clique

Decision versus Search versus Optimization

Approximation versus Exact Algorithms

Homework

1. Suppose you had available a decision algorithm for Vertex Cover that ran in T(n) time. (a) How would you use it to solve the optimization version of the problem? (b) What is the time complexity of your method?

2. Consider the Traveling Salesman Problem. (a) How would you approximate an optimal solution in polynomial time if the triangle inequality holds? (Hint: look up Christofides algorithm.) (b) What worst-case guarantee can you provide if the triangle inequality does not hold?