基于模分解的部分传递定向和同时传递定向
Partial and Simultaneous Transitive Orientations via Modular Decomposition
摘要：
几何图形类的识别问题的一个自然推广是将子图的表示扩展为整个图的表示的问题。一个相关的问题是找到多个输入图的表示，这些输入图在由输入图共享的子图上重合。一个常见的限制是向日葵的情况下，共享图是相同的每对输入图。这些问题转化为可比性图的设置，其中表示对应于其边缘的传递方向。我们使用模块分解，以提高运行时间的方向扩展问题和向日葵方向问题的线性时间。我们应用这些结果，以提高运行时间的部分表示问题和向日葵的情况下，同时表示问题的置换图的线性时间。我们也给出了循环置换图上的第一个有效算法。
英文摘要：
A natural generalization of the recognition problem for a geometric graph class is the problem of extending a representation of a subgraph to a representation of the whole graph. A related problem is to find representations for multiple input graphs that coincide on subgraphs shared by the input graphs. A common restriction is the sunflower case where the shared graph is the same for each pair of input graphs. These problems translate to the setting of comparability graphs where the representations correspond to transitive orientations of their edges. We use modular decompositions to improve the runtime for the orientation extension problem and the sunflower orientation problem to linear time. We apply these results to improve the runtime for the partial representation problem and the sunflower case of the simultaneous representation problem for permutation graphs to linear time. We also give the first efficient algorithms for these problems on circular permutation graphs.
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。
