Primal-Dual Schema and Local Ratio

Ding-Zhu Du (), Ker-I Ko () and Xiaodong Hu ()
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Ding-Zhu Du: University of Texas at Dallas
Ker-I Ko: State University of New York at Stony Brook
Xiaodong Hu: Academy of Mathematics and Systems Science Chinese Academy of Sciences

Chapter 8 in Design and Analysis of Approximation Algorithms, 2012, pp 297-337 from Springer

Abstract: Abstract 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.

Keywords: Feasible Solution; Network Design Problem; Local Ratio; Dual Linear Program; Complementary Slackness Condition (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/978-1-4614-1701-9_8

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