Lec . 2 : Approximation Algorithms for NP - hard Problems ( Part II )

We will continue the survey of approximation algorithms in this lecture. First, we will discuss a (1+ε)-approximation algorithm for Knapsack in time poly(n, 1/ε). We will then see applications of some heavy hammers such as linear programming (LP) and semi-definite programming (SDP) towards approximation algorithms. More specifically, we will see LPbased approximation for MAXSAT and MAXCUT. In the following lecture, we will see a SDP-based algorithm for MAXCUT. The references for this lecture include Lecture 1 of the DIMACS tutorial on Limits of approximation [HC09], Lectures 2, 3 and 4 of Sudan’s course on inapproximability at MIT [Sud99], and Section 8 from Vazirani’s book on Approximation Algorithms [Vaz04].