支配集与独立集重构的参数化复杂度
Parameterized Complexities of Dominating and Independent Set Reconfiguration
AI总结：
本文解决了由令牌数量参数化的独立集和支配集重构问题的参数化复杂度，证明了不同移动限制下的完全性，并证明令牌滑动与跳跃在pl-归约下等价。
摘要：
我们解决了由令牌数量参数化的独立集重构和支配集重构若干变体的参数化复杂度问题。我们证明，当对移动次数没有限制时，这两个问题都是 XL 完全的；当序列的最大长度 $\ell$ 在输入中以二进制给出时，它们是 XNL 完全的；当 $\ell$ 以一元给出时，它们是 XNLP 完全的。当 $\ell$ 也是参数时，已知这两个问题分别是 $\mathrm{W}[1]$-hard 和 $\mathrm{W}[2]$-hard 的。我们通过证明它们属于这些类来补全了这一图景。此外，我们证明对于我们考虑的所有变体，令牌滑动和令牌跳跃在 pl-归约下是等价的。我们引入了令牌跳跃和令牌滑动的划分变体，并在四个变体之间给出了能够精确控制令牌数量和重构序列长度的 pl-归约。
英文摘要：
We settle the parameterized complexities of several variants of independent set reconfiguration and dominating set reconfiguration, parameterized by the number of tokens. We show that both problems are XL-complete when there is no limit on the number of moves, XNL-complete when a maximum length $\ell$ for the sequence is given in binary in the input, and XNLP-complete when $\ell$ is given in unary. The problems were known to be $\mathrm{W}[1]$- and $\mathrm{W}[2]$-hard respectively when $\ell$ is also a parameter. We complete the picture by showing membership in those classes. Moreover, we show that for all the variants that we consider, token sliding and token jumping are equivalent under pl-reductions. We introduce partitioned variants of token jumping and token sliding, and give pl-reductions between the four variants that have precise control over the number of tokens and the length of the reconfiguration sequence.
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。
