A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
Strengthening integrality gaps for capacitated network design and covering problems
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A unified approach to approximating resource allocation and scheduling
Journal of the ACM (JACM)
Approximating covering integer programs with multiplicity constraints
Discrete Applied Mathematics
Resource optimization in QoS multicast routing of real-time multimedia
IEEE/ACM Transactions on Networking (TON)
On the approximability of some network design problems
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Weighted geometric set cover via quasi-uniform sampling
Proceedings of the forty-second ACM symposium on Theory of computing
FOCS '10 Proceedings of the 2010 IEEE 51st Annual Symposium on Foundations of Computer Science
Bin packing via discrepancy of permutations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
On column-restricted and priority covering integer programs
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Weighted capacitated, priority, and geometric set cover via improved quasi-uniform sampling
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Recently, Chakrabarty et al. [5] initiated a systematic study of capacitated set cover problems, and considered the question of how their approximability relates to that of the uncapacitated problem on the same underlying set system. Here, we investigate this connection further and give several results, both positive and negative. In particular, we show that if the underlying set system satisfies a certain hereditary property, then the approximability of the capacitated problem is closely related to that of the uncapacitated version. We also give related lower bounds, and show that the hereditary property is necessary to obtain non-trivial results. Finally, we give some results for capacitated covering problems on set systems with low hereditary discrepancy and low VC dimension.