Asymptotics of the chromatic index for multigraphs
Journal of Combinatorial Theory Series B
There is no asymptotic PTAS for two-dimensional vector packing
Information Processing Letters
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A sublinear bound on the chromatic index of multigraphs
Discrete Mathematics
Approximation algorithms
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
Probability and Computing: Randomized Algorithms and Probabilistic Analysis
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
An APTAS for Generalized Cost Variable-Sized Bin Packing
SIAM Journal on Computing
Asymptotic fully polynomial approximation schemes for variants of open-end bin packing
Information Processing Letters
AFPTAS Results for Common Variants of Bin Packing: A New Method for Handling the Small Items
SIAM Journal on Optimization
Bin packing via discrepancy of permutations
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bin packing with general cost structures
Mathematical Programming: Series A and B
The entropy rounding method in approximation algorithms
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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We consider set covering problems where the underlying set system satisfies a particular replacement property w.r.t. a given partial order on the elements: Whenever a set is in the set system then a set stemming from it via the replacement of an element by a smaller element is also in the set system. Many variants of Bin Packing that have appeared in the literature are such set covering problems with ordered replacement. We provide a rigorous account on the additive and multiplicative integrality gap and approximability of set covering with replacement. In particular we provide a polylogarithmic upper bound on the additive integrality gap that also yields a polynomial time additive approximation algorithm if the linear programming relaxation can be efficiently solved. We furthermore present an extensive list of covering problems that fall into our framework and consequently have polylogarithmic additive gaps as well.