发表机构
University of Bucharest; National Institute for Research and Development in Informatics（布加勒斯特大学; 罗马尼亚信息学研究与发展中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究匹配-匹配谜题的计算复杂性，证明二色NP完全性，蜘蛛图上颜色参数W[1]-难，腿长≤2时固定参数可解，腿长=3时NP完全。
AI 中文摘要
网络模体和彩色局部交互模式为描述复杂网络的结构提供了有用的方式。受逆实现视角的启发，我们研究将颜色分配给固定图的顶点，使其边实现预先给定的彩色成对交互多重集的问题。该问题由Iburi和Uehara引入的匹配-匹配谜题形式化。我们研究其计算复杂性如何依赖于颜色数量以及宿主图的结构。我们首先证明，即使没有顶点被预着色且图的最大度为三，仅用两种颜色，匹配-匹配问题也是NP完全的。然后我们关注蜘蛛图。我们证明，即使在仅身体被预着色的蜘蛛图上，该问题以颜色数量为参数也是W[1]-难的。相比之下，对于腿长至多为二的蜘蛛图，我们给出了以颜色数量为参数的固定参数可处理算法，允许任意预着色。最后，我们证明当允许预着色时，对于所有腿长恰好为三的蜘蛛图，该问题是NP完全的。
英文摘要
Network motifs and colored local interaction patterns provide a useful way to describe the structure of complex networks. Motivated by an inverse realization perspective, we study the problem of assigning colors to the vertices of a fixed graph so that its edges realize a prescribed multiset of colored pairwise interactions. This problem is formalized by the Matching-Match Puzzle, introduced by Iburi and Uehara. We investigate how its computational complexity depends on the number of colors and on the structure of the host graph. We first prove that Matching-Match is NP-complete with only two colors, even when no vertex is precolored and the graph has maximum degree three. We then focus on spiders. We show that the problem is W[1]-hard parameterized by the number of colors even on spiders with only the body precolored. In contrast, for spiders whose legs have length at most two, we give a fixed-parameter tractable algorithm parameterized by the number of colors, allowing arbitrary precoloring. Finally, we prove NP-completeness for spiders whose legs all have length exactly three when precoloring is allowed.
