Graduate Algorithms

In this lecture, we covered the simple 2-approximation for computing the vertex cover. In class, we proved the approximation ratio based on a simple local argument: namely that for each pair of vertices the algorithm chooses, OPT must pick at least one of them. We also looked at the problem of minimizing makespan which has the distinction of yielding one of the very first approximation algorithms, a 2-1/m approximation due to Ron Graham in 1966.

In both of the above cases, we emphasized the need for a lower bound on OPT, so as to reason about the approximation ratio guaranteed by our method. We were able to construct such a lower bound directly by inspection of the input or the algorithm. We then moved onto the problem of SET COVER, where such a lower bound is much harder to come by, and is constructed bit by bit from the steps of the algorithm.

The treatment of the SET COVER analysis in class differs slightly from the textbook. These notes are a useful guide to the method of analysis we used in class.

This entry was posted on Monday, October 15th, 2007 at 1:01 am and is filed under Lectures, News.