Bottleneck subset-type restricted matching problems

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 $$\hbox {P} = \hbox {NP}$$ .