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: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=750520
• 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，这意味着即使用非常快的计算机也不能在合理的时间内解决它们。然而，在许多应用中，例如调度和设施选址，情况的结构保证只会出现某些图。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-Hard问题构造一个有效的算法。这些观察结果激励了我在算法设计和图类中的问题复杂性方面的研究。我研究在应用中出现的或对问题的解决方案有洞察力的图类，并利用它们的性质设计多项式时间算法或证明这样的算法不太可能存在。目标是了解问题和图属性之间的相互作用，并找到适用于大类图的高效算法。这项研究增加了关于问题和图的知识，并具有实际影响，因为图算法在不同的应用中形成了计算机程序的基础。