In this chapter we will introduce the method of dual fitting, which helps analyze combinatorial algorithms using LP-duality theory. Using this method, we will present an alternative analysis of the natural greedy algorithm (Algorithm 2.2) for the set cover problem (Problem 2.1). Recall that in Section 2.1 we deferred giving the lower bounding method on which this algorithm was based. We will provide the answer below. The power of this approach will become apparent when we show the ease with which it extends to solving several generalizations of the set cover problem (see Section 13.2).
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