title: an algorithm to find the minimum size set cover for the Set-cover problem
body: <p>In the Set Covering problem, we are given a universe U, such that |U|=n, and sets S1,……,Sk are subsets of U. A set cover is a collection C of some of the sets from S1,……,Sk whose union is the entire universe U. </p>
  
  <p>I'm trying to come up with an algorithm that will find the minimum number of set cover so that I can show that the greedy algorithm for set covering sometimes finds more sets.</p>
  
  <p>Following is what I came up with:</p>
  
  <p>repeat for each set.
  1. Cover&lt;-Seti (i=1,,,n)
  2. if a set is not a subset of any other sets, then take take that set into cover.</p>
  
  <p>but it's not working for some instances.
  Please help me figure out an algorithm to find the minimum set cover. </p>
  
  <p>I'm still having problem find this algorithm online. Anyone has any suggestion? </p>