Algorithms and complexity for structured graph classes

结构化图类的算法和复杂性

• 批准号: RGPIN-2016-04849
• 负责人: Stewart, Lorna
• 金额: $ 1.6万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=665965
• 关键词: Algorithms; complexity; structured; graph; classes

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.**

许多图问题是NP难的，这意味着即使是非常快的计算机也无法在合理的时间内解决它们。然而，在许多应用中，例如调度和设施定位，情况的结构保证只有某些图会出现。有时，如果事先知道需要处理的图，就有可能为NP难问题构造一个有效的算法。这些观察激励我的研究在算法设计和问题的复杂性类图。我研究类的图形出现在应用程序中，或提供洞察到一个问题的解决方案，并利用它们的属性来设计多项式时间算法或证明这种算法是不可能存在的。我们的目标是了解问题和图形属性之间的相互作用，并找到有效的算法，工作在大类的图形。这项研究增加了关于问题和图形的知识，并具有实际影响，因为图形算法构成了各种应用程序的计算机程序的基础。