Homework 1: Due thursday Jan 19.
The Set Cover Problem is, given a collection of sets, to choose some of those sets so that every element is in some chosen set. The goal is to minimize the number of chosen sets. Unless P=NP, there is no o(log n)-approximation algorithm for set cover, where n is the number of elements in the problem instance.
Using this latter fact, show that (unless P=NP) there is no o(log n)-approximation algorithm for the Directed Steiner tree problem, by giving an approximation-preserving reduction from Set Cover to Directer Steiner tree.
Turn in a careful write-up of your proof.