Abstract
We introduce two problems related to finding in a weighted complete bipartite graph a special matching such that the maximum weight of its some subsets is minimal. We discuss their applications and show the strong NP-hardness of both problems. We show that one problem cannot be approximated in polynomial time within a factor of less than 2 and another problem cannot be approximated in polynomial time within a factor of \(\alpha (n)\), where \(\alpha (n)\) is an arbitrary polynomial-time computable function, unless \(\hbox {P} = \hbox {NP}\).
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Duginov, O. Bottleneck subset-type restricted matching problems. J Comb Optim 40, 796–805 (2020). https://doi.org/10.1007/s10878-020-00627-8
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DOI: https://doi.org/10.1007/s10878-020-00627-8