最佳匹配图修改问题的复杂性
Complexity of modification problems for best match graphs
摘要：
最佳匹配图（BMG）是顶点着色的有向图，其被引入以对来自不同物种（颜色）的基因（顶点）之间的关系进行建模，给定假设未知的底层进化树。在实际应用中，BMG是从序列相似性数据中估计的。测量噪声和近似误差通常会导致经验确定的图形，一般违反BMG的特性。BMG的弧修改问题的目的是纠正这种违规行为，从而提供了一种手段，以改善最佳匹配数据的初始估计。我们在这里表明，弧删除，弧完成和弧编辑问题的BMG是NP-完全的，他们可以制定和解决整数线性规划。为此，我们提供了一种新的表征BMG的三元组（二叉树上的三叶）和表征BMG的两种颜色的禁用子图。
英文摘要：
Best match graphs (BMGs) are vertex-colored directed graphs that were introduced to model the relationships of genes (vertices) from different species (colors) given an underlying evolutionary tree that is assumed to be unknown. In real-life applications, BMGs are estimated from sequence similarity data. Measurement noise and approximation errors usually result in empirically determined graphs that in general violate characteristic properties of BMGs. The arc modification problems for BMGs aim at correcting such violations and thus provide a means to improve the initial estimates of best match data. We show here that the arc deletion, arc completion and arc editing problems for BMGs are NP-complete and that they can be formulated and solved as integer linear programs. To this end, we provide a novel characterization of BMGs in terms of triples (binary trees on three leaves) and a characterization of BMGs with two colors in terms of forbidden subgraphs.
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。
