查找和计数顶点着色子树
Finding and counting vertex-colored subtrees
摘要：
本文研究的问题源于Lacroix等人在生物网络背景下提出的图模体问题。问题是判定一个顶点着色图是否有一个连通子图，其颜色等于给定的颜色集$M$。这是一个图形模式匹配问题的变体，其中模式发生的结构并不重要，唯一的要求是连通性。使用Koutis等人最近提出的代数框架，我们得到了新的FPT算法的图形图案和变种，改善了运行时间。我们还得到了这个问题的计数版本的结果，证明了计数问题是FPT，如果M是一个集，但成为W[1]-困难，如果M是一个多集与两个颜色。最后，我们提出了一个实验评估这种方法在真实的数据集，显示其性能与现有的软件相比毫不逊色。
英文摘要：
The problems studied in this article originate from the Graph Motif problem introduced by Lacroix et al. in the context of biological networks. The problem is to decide if a vertex-colored graph has a connected subgraph whose colors equal a given multiset of colors $M$. It is a graph pattern-matching problem variant, where the structure of the occurrence of the pattern is not of interest but the only requirement is the connectedness. Using an algebraic framework recently introduced by Koutis et al., we obtain new FPT algorithms for Graph Motif and variants, with improved running times. We also obtain results on the counting versions of this problem, proving that the counting problem is FPT if M is a set, but becomes W[1]-hard if M is a multiset with two colors. Finally, we present an experimental evaluation of this approach on real datasets, showing that its performance compares favorably with existing software.
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。
