Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Algorithms for capacitated rectangle stabbing and lot sizing with joint set-up costs
ACM Transactions on Algorithms (TALG)
Exact Algorithms for Set Multicover and Multiset Multicover Problems
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Capacitated domination problem
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Dynamic programming based algorithms for set multicover and multiset multicover problems
Theoretical Computer Science
Primal-dual schema for capacitated covering problems
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Capacitated domination and covering: a parameterized perspective
IWPEC'08 Proceedings of the 3rd international conference on Parameterized and exact computation
Generalized machine activation problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Capacitated domination: constant factor approximations for planar graphs
ISAAC'11 Proceedings of the 22nd international conference on Algorithms and Computation
Set cover revisited: hypergraph cover with hard capacities
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A model for minimizing active processor time
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
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We consider the classical vertex cover and set cover problems with hard capacity constraints. This means that a set (vertex) can cover only 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 which 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 that is based on randomized rounding with alterations. We prove that the weighted version is at least as hard as the set cover problem, yielding 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 [Combinatorica, 2 (1982), pp. 385-393] on submodular set cover. We provide here a simple and intuitive proof for this bound.