Fixed-parameter tractable (FPT) algorithms have been successfully applied to many intractable problems -- with a focus on decision and optimization problems. Their aim is to confine the exponential explosion to some parameter, while the time complexity only depends polynomially on the instance size. In contrast, intractable enumeration problems have received comparatively little attention so far. The goal of this work is to study how FPT decision algorithms could be turned into FPT enumeration algorithms. We thus inspect several fundamental approaches for designing FPT decision or optimization algorithms and we present ideas how they can be extended to FPT enumeration algorithms.

翻译：固定参数可解（FPT）算法已成功应用于许多难解问题——主要集中在决策和优化问题上。其目标是将指数爆炸限制在某个参数内，而时间复杂度仅与实例大小呈多项式依赖。相比之下，难解的枚举问题迄今受到的关注相对较少。本工作的目标是研究如何将FPT决策算法转化为FPT枚举算法。为此，我们考察了设计FPT决策或优化算法的几种基本方法，并提出如何将其扩展为FPT枚举算法的思路。