信道分配问题的紧下界
Tight lower bound for the channel assignment problem
摘要：
我们研究了信道分配问题的复杂性。一个主要的开放性问题是，信道分配是否允许一个$O(c^n)$时间算法，对于一个恒定的$c$独立的边缘上的权重。我们回答这个问题的否定，即我们表明，没有$2^{o(n\log n)}$时间算法解决信道分配，除非指数时间假设失败。请注意，目前最著名的算法工作在时间$O^*(n!) = 2^{O(n\log n)}$，所以我们的下限是紧的。
英文摘要：
We study the complexity of the Channel Assignment problem. A major open problem asks whether Channel Assignment admits an $O(c^n)$-time algorithm, for a constant $c$ independent of the weights on the edges. We answer this question in the negative i.e. we show that there is no $2^{o(n\log n)}$-time algorithm solving Channel Assignment unless the Exponential Time Hypothesis fails. Note that the currently best known algorithm works in time $O^*(n!) = 2^{O(n\log n)}$ so our lower bound is tight.
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。
