On the Equivalence between the Primal-Dual Schema and the Local-Ratio Technique [chapter]

Reuven Bar-Yehuda, Dror Rawitz
2001 Lecture Notes in Computer Science  
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 divised 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 context of maximization algorithms. Subsequently, the nature of
more » ... the connection between the two paradigms was posed as an open question by Williamson [35]. In this paper we answer this question by showing that the two paradigms are equivalent. The equivalence between the paradigms is constructive, and it implies that the integrality gap of an integer program serves as a bound to the approximation ratio when working with the local ratio technique.
doi:10.1007/3-540-44666-4_7 fatcat:prueocv4mjhznkmmkjvijxjzru