1. On the Equivalence between the Primal-Dual Schema and the Local Ratio Technique.
- Author
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Bar-Yehuda, Reuven and Rawitz, Dror
- Subjects
- *
ALGORITHMS , *MATHEMATICS , *LINEAR programming , *MATHEMATICAL optimization , *ALGEBRAIC number theory , *MATHEMATICAL analysis - Abstract
We discuss two approximation paradigms that were used to construct many approximation algorithms during the last two decades, the primal-dual schema and the local ratio technique. Recently, primal-dual algorithms were devised by first constructing a local ratio algorithm and then transforming it into a primal-dual algorithm. This was done in the case of the $2$-approximation algorithms for the feedback vertex set problem and in the case of the first primal-dual algorithms for maximization problems. Subsequently, the nature of the connection between the two paradigms was posed as an open question by Williamson [Math. Program., 91 (2002), pp. 447--478]. In this paper we answer this question by showing that the two paradigms are equivalent. [ABSTRACT FROM AUTHOR]
- Published
- 2005
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