Rich Toolset of Parameterized Complexity Theory in AI Research: A Survey

In this article, we explore how a powerful tool called parameterized complexity theory can help us better understand the computational complexity of problems in artificial intelligence. We discuss how this approach has been successfully applied to various areas of research, including hedonic games, integer programming, data completion, and social optimization of transportation networks.
To illustrate the potential of parameterized complexity theory, we provide examples of intractable instances of centralized routing of agents across a network in a socially optimal manner, which are often too difficult for classical computational complexity theory to handle. We also acknowledge the support of the Austrian Science Foundation and SERB-DST for the research presented in the article.
To demystify complex concepts, we use everyday language and analogies to explain how parameterized complexity theory can help identify the structural properties of an input that give rise to fixed-parameter algorithms. For instance, we compare the process of centralized routing with individual transportation, highlighting how public transportation is usually planned and routed centrally for its lower environmental impact, whereas individual transportation is more fragmented and chaotic.
Throughout the article, we strive to strike a balance between simplicity and thoroughness, capturing the essence of the research without oversimplifying it. We hope that this summary will help readers better understand the significance of parameterized complexity theory in tackling computationally intractable problems in artificial intelligence.