有理问题的强NP-完全性
On Strong NP-Completeness of Rational Problems
摘要：
在所有权值和利润均为整数的情况下，对划分问题、0 -1子集和问题、无界子集和问题、0-1背包问题和无界背包问题及其多个变形的计算复杂性进行了研究。我们在这里重新检查的计算复杂性的所有这些问题的设置中的权重和利润是允许的任何有理数。我们表明，所有这些问题在这种设置成为强NP-完全，因此，没有伪多项式算法可以解决它们，除非P=NP。尽管这个结果，我们表明，他们仍然承认一个完全多项式时间近似计划。
英文摘要：
The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were assumed to be integers. We re-examine here the computational complexity of all these problems in the setting where the weights and profits are allowed to be any rational numbers. We show that all of these problems in this setting become strongly NP-complete and, as a result, no pseudo-polynomial algorithm can exist for solving them unless P=NP. Despite this result we show that they all still admit a fully polynomial-time approximation scheme.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
