Let XNLP be the class of parameterized problems such that an instance of size $n$ with parameter $k$ can be solved nondeterministically in time $f(k)n^{O(1)}$ and space $f(k)\log(n)$ (for some computable function $f$). We give a wide variety of XNLP-complete problems, such as {\sc List Coloring} and {\sc Precoloring Extension} with pathwidth as parameter, {\sc Scheduling of Jobs with Precedence Constraints}, with both number of machines and partial order width as parameter, {\sc Bandwidth} and variants of {\sc Weighted CNF-Satisfiability} and reconfiguration problems. In particular, this implies that all these problems are $W[t]$-hard for all $t$. This also answers a long standing question on the parameterized complexity of the {\sc Bandwidth} problem.
翻译：让 XNLP 成为参数化问题的类别, 如此一来, 一个大小为$n的参数 $k$ 的参数就可以在时间上以非决定性的方式解决 $f( k)n ⁇ O(1)}$ and space $f( k)\log( n)$( 对于某些可计算函数 $f) 。 我们给出了各种各样的 XNLP 完整的问题, 比如 ~ sc List Coloring } 和 ~ sc prec 彩色扩展 }, 以路径为参数, ~sc 排练带有优先限制的工作 }, 机器的数量和部分顺序宽度作为参数, ~sc Bandwidth}, 以及 ~ sc wec CDF- Sabletifility 和重新配置问题 。 特别是, 这意味着所有这些问题对于美元来说都是 $[ t] $( t) 。 这还回答了关于 spandwith} 问题的参数化复杂性的长期问题 。
相关内容
微信扫码咨询专知VIP会员