On the Equivalence between the Primal-Dual Schema and the Local-Ratio Technique
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Local ratio: A unified framework for approximation algorithms. In Memoriam: Shimon Even 1935-2004
ACM Computing Surveys (CSUR)
Primal-dual schema for capacitated covering problems
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
How well can primal-dual and local-ratio algorithms perform?
ACM Transactions on Algorithms (TALG)
Using fractional primal-dual to schedule split intervals with demands
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Theoretical Computer Science
Using fractional primal-dual to schedule split intervals with demands
Discrete Optimization
Local ratio with negative weights
Operations Research Letters
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In recent years approximation algorithms based on primal-dual methods have been successfully applied to a broad class of discrete optimization problems. In this paper, we propose a generic primal-dual framework to design and analyze approximation algorithms for integer programming problems of the covering type that uses valid inequalities in its design. The worst-case bound of the proposed algorithm is related to a fundamental relationship (called strength) between the set of valid inequalities and the set of minimal solutions to the covering problems. In this way, we can construct an approximation algorithm simply by constructing the required valid inequalities. We apply the proposed algorithm to several problems, such as covering problems related to totally balanced matrices, cyclic scheduling, vertex cover, general set covering, intersections of polymatroids, and several network design problems attaining (in most cases) the best worst-case bound known in the literature.