Lecture 2 , 3 ( Sept 13 and 15 , 2011 ) : Set Cover , Introduction to LP

Note that vertex cover is a special case of set cover where U is the set of all edges and each vertex v is a subset in S which contains all edges incident to v. In this case, each element is in exactly two subsets in S. We present a greedy approximation algorithm for Set Cover. This is probably the most natural greedy algorithm for this problem. The idea is, at each iteration pick a set where the ratio of the cost of the set divided by the number of new elements it covers is minimized. This general idea of “covering” elements iteratively by finding good partial solutions has been used in many other problems. The analysis of set-cover (we present here) can typically be extended to those other covering algorithms that behave similarly.