Abstract
The \(k\)-partitioning problem with partition matroid constraint is to partition the union of \(k\) given sets of size \(m\) into \(m\) sets such that each set contains exactly one element from each given set. With the objective of minimizing the maximum load, we present an efficient polynomial time approximation scheme (EPTAS) for the case where \(k\) is a constant and a full polynomial time approximation scheme (FPTAS) for the case where \(m\) is a constant; with the objective of maximizing the minimum load, we present a \(\frac{1}{k-1}\)-approximation algorithm for the general case, an EPTAS for the case where \(k\) is a constant; with the objective of minimizing the \(l_p\)-norm of the load vector, we prove that the layered LPT algorithm (Wu and Yao in Theor Comput Sci 374:41–48, 2007) is an all-norm 2-approximation algorithm.
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Acknowledgments
The authors are grateful to the two anonymous referees whose comments and suggestions have led to a substantially improved presentation for the paper. The work is supported by the Tianyuan Fund for Mathematics of the National Natural Science Foundation of China [No. 11126315] and the National Natural Science Foundation of China [No. 61063011].
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Li, W., Li, J. Approximation algorithms for \(k\)-partitioning problems with partition matroid constraint. Optim Lett 8, 1093–1099 (2014). https://doi.org/10.1007/s11590-013-0637-2
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DOI: https://doi.org/10.1007/s11590-013-0637-2