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

We discuss two approximation paradigms that were used to construct many approxi- mation 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.