Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Primal-dual based distributed algorithms for vertex cover with semi-hard capacities
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Dependent rounding and its applications to approximation algorithms
Journal of the ACM (JACM)
An improved approximation algorithm for vertex cover with hard capacities
Journal of Computer and System Sciences
An improved approximation algorithm for vertex cover with hard capacities
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Approximation of partial capacitated vertex cover
ESA'07 Proceedings of the 15th annual European conference on Algorithms
AdCell: ad allocation in cellular networks
ESA'11 Proceedings of the 19th European conference on Algorithms
Approximation of Partial Capacitated Vertex Cover
SIAM Journal on Discrete Mathematics
Approximation algorithms for capacitated rectangle stabbing
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
Submodular integer cover and its application to production planning
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
The multi-radius cover problem
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Parameterized complexity of generalized vertex cover problems
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Journal of Discrete Algorithms
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We consider the classical vertex cover and set cover problems with the addition of hard capacity constraints. This means that a set (vertex) can only cover a limited number of its elements (adjacent edges) and the number of available copies of each set (vertex) is bounded. This is a natural generalization of the classical problems that also captures resource limitations in practical scenarios.We obtain the following results. For the unweighted vertex cover problem with hard capacities we give a 3-approximation algorithm which is based on randomized rounding with alterations. We prove that the weighted version is at least as hard as the set cover problem. This is an interesting separation between the approximability of weighted and unweighted versions of a "natural" graph problem. A logarithmic approximation factor for both the set cover and the weighted vertex cover problem with hard capacities follows from the work of Wolsey [23] on submodular set cover. We provide in this paper a simple and intuitive proof for this bound.