Algorithms and complexity for structured graph classes

许多图形问题是np困难的，这意味着即使是非常快的计算机也不能在合理的时间内解决它们。然而，在许多应用程序中，例如调度和设施位置，情况的结构保证只会出现某些图形。有时，如果事先知道需要处理的图的某些信息，就有可能为np困难问题构建一个有效的算法。这些观察激发了我对算法设计和图类问题复杂性的研究。我研究应用程序中出现的图形类，或者对问题的解决方案提供见解，并利用它们的属性来设计多项式时间算法，或者证明这种算法不太可能存在。目标是理解问题和图属性之间的相互作用，并找到在大型图类上工作的有效算法。这项研究增加了关于问题和图的知识，并具有实际影响，因为图算法构成了各种应用中计算机程序的基础

Many graph problems are NP-hard, which means that they cannot be solved in a reasonable amount of time even by a very fast computer. However, in many applications, such as scheduling and facility location, the structure of the situation guarantees that only certain graphs will arise. And sometimes it is possible to construct an efficient algorithm for an NP-hard problem if something is known in advance about the graphs that need to be handled. These observations motivate my research in algorithm design and problem complexity in classes of graphs. I study classes of graphs that arise in applications or that give insight into a problem's solution, and make use of their properties to design polynomial time algorithms or to prove that such algorithms are unlikely to exist. The goal is to understand the interplay between problems and graph properties, and to find efficient algorithms that work on large classes of graphs. This research adds to knowledge about problems and graphs, and has practical impact since graph algorithms form the basis of computer programs in diverse applications.**