Abstract
We consider a variant of the generalized assignment problem (GAP) where the items have unit size and the amount of space used in each bin is restricted to be either zero (if the bin is not opened) or above a given lower bound (a minimum quantity). This problem is known to be strongly NP-complete and does not admit a polynomial time approximation scheme (PTAS).
By using randomized rounding, we obtain a randomized 3.93-approximation algorithm, thereby providing the first nontrivial approximation result for this problem.
An Erratum for this chapter can be found at http://dx.doi.org/10.1007/978-3-642-40313-2_74
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Bender, M., Thielen, C., Westphal, S. (2013). A Constant Factor Approximation for the Generalized Assignment Problem with Minimum Quantities and Unit Size Items. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_14
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DOI: https://doi.org/10.1007/978-3-642-40313-2_14
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