On the equivalence between the primal-dual schema and the local ratio technique

Reuven Bar-Yehuda, Dror Rawitz

Research output: Contribution to journalArticlepeer-review

46 Scopus citations

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.

Original languageEnglish
Pages (from-to)762-797
Number of pages36
JournalSIAM Journal on Discrete Mathematics
Volume19
Issue number3
DOIs
StatePublished - 2005
Externally publishedYes

Keywords

  • Approximation algorithms
  • Combinatorial optimization
  • Covering problems
  • Local ratio
  • Primal-dual

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