Primal-Dual Schema and Local Ratio
Based on the duality theory of linear programming, a new approximation technique, called the primal-dual schema, has been developed. With this technique, we do not need to compute the optimal solution of the relaxed linear program in order to get an approximate solution of the integer program. Thus, we can reduce the running time of many linear programming–based approximation algorithms from O(n3) to at most O(n2). Moreover, this method can actually be formulated in an equivalent form, called the local ratio method, which does not require the knowledge of the theory of linear programming. In this chapter, we study these two techniques and their relationship.
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