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Bottleneck subset-type restricted matching problems
Journal of Combinatorial Optimization ( IF 1 ) Pub Date : 2020-07-20 , DOI: 10.1007/s10878-020-00627-8
Oleg Duginov

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 \(\hbox {P} = \hbox {NP}\).

中文翻译:

瓶颈子集类型受限匹配问题

我们介绍了两个有关在加权完整二部图中找到特殊匹配的问题,这些匹配使得其某些子集的最大权重最小。我们讨论了它们的应用,并展示了这两个问题的强NP硬度。我们表明,一个问题不能在多项式时间内以小于2的因数近似,而另一个问题不能在多项式时间内以\(\ alpha(n)\)的因数近似,其中\(\ alpha(n)\ )是任意的多项式时间可计算函数,除非\(\ hbox {P} = \ hbox {NP} \)
更新日期:2020-07-20
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