A fast approximation algorithm for the multicovering problem
Discrete Applied Mathematics
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A threshold of ln n for approximating set cover (preliminary version)
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of computing
The primal-dual method for approximation algorithms and its application to network design problems
Approximation algorithms for NP-hard problems
Improved performance of the greedy algorithm for partial cover
Information Processing Letters
Using homogenous weights for approximating the partial cover problem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Approximation algorithms
Capacitated vertex covering with applications
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Covering Problems with Hard Capacities
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Approximation Algorithms for Partial Covering Problems
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
The t-Vertex Cover Problem: Extending the Half Integrality Framework with Budget Constraints
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Improved Approximation Algorithms for the Partial Vertex Cover Problem
APPROX '02 Proceedings of the 5th International Workshop on Approximation Algorithms for Combinatorial Optimization
A Unified Local Ratio Approximation of Node-Deletion Problems (Extended Abstract)
ESA '96 Proceedings of the Fourth Annual European Symposium on Algorithms
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Tight Approximation Results for General Covering Integer Programs
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Approximation algorithms for combinatorial problems
Journal of Computer and System Sciences
On approximation of the submodular set cover problem
Operations Research Letters
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Suppose there are a set of suppliers i and a set of consumers j with demands bj, and the amount of products that can be shipped from i to j is at most cij. The amount of products that a supplier i can produce is an integer multiple of its capacity κi, and every production of κi products incurs the cost of wi. The capacitated supply-demand (CSD) problem is to minimize the production cost of ∑iwixi such that all the demands (or the total demand requirement specified separately) at consumers are satisfied by shipping products from the suppliers to them. To capture the core structural properties of CSD in a general framework, we introduce the submodular integer cover (SIC) problem, which extends the submodular set cover (SSC) problem by generalizing submodular constraints on subsets to those on integer vectors. Whereas it can be shown that CSD is approximable within a factor of O(log(maxi,κi)) by extending the greedy approach for SSC to CSD, we first generalize the primal-dual approach for SSC to SIC and evaluate its performance. One of the approximation ratios obtained for CSD from such an approach is the maximum number of suppliers that can ship to a single consumer; therefore, the approximability of CSD can be ensured to depend only on the network (incidence) structure and not on any numerical values of input capacities κi,bj,cij. The CSD problem also serves as a unifying framework for various types of covering problems, and any approximation bound for CSD holds for set cover generalized simultaneously into various directions. It will be seen, nevertheless, that our bound matches (or nearly matches) the best result for each generalization individually. Meanwhile, this bound being nearly tight for standard set cover, any further improvement, even if possible, is doomed to be a marginal one.