通过中间相遇方法优化渠道
Assigning channels via the meet-in-the-middle approach
摘要：
我们研究了信道分配问题的复杂性。通过应用中间相遇方法，我们得到了一个在时间上运行的$\ell$有界信道分配算法（当边缘权重由$\ell$有界时）$O^*((2\sqrt{\ell+1})^n)$。这是第一个打破$(O(\ell))^n$障碍的算法。我们将该算法推广到计数型，代价是多项式因子略高。一个主要的开放问题是，对于独立于$\ell$的恒定$c$，信道分配是否允许$O(c^n)$时间算法。我们考虑一个类似的问题，广义T-着色，CSP问题，推广\CA。我们表明，广义T-着色不承认一个$2^{2^{o\left(\sqrt{n}\right)}} {\rm poly}(r)$时间算法，其中$r$是实例的大小。
英文摘要：
We study the complexity of the Channel Assignment problem. By applying the meet-in-the-middle approach we get an algorithm for the $\ell$-bounded Channel Assignment (when the edge weights are bounded by $\ell$) running in time $O^*((2\sqrt{\ell+1})^n)$. This is the first algorithm which breaks the $(O(\ell))^n$ barrier. We extend this algorithm to the counting variant, at the cost of slightly higher polynomial factor. A major open problem asks whether Channel Assignment admits a $O(c^n)$-time algorithm, for a constant $c$ independent of $\ell$. We consider a similar question for Generalized T-Coloring, a CSP problem that generalizes \CA. We show that Generalized T-Coloring does not admit a $2^{2^{o\left(\sqrt{n}\right)}} {\rm poly}(r)$-time algorithm, where $r$ is the size of the instance.
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。
