Paradigms for Parameterized Enumeration

Parameterized Enumeration with Ordering

The classes Delay-FPT and Total-FPT recently have been introduced into parameterized complexity in order to capture the notion of efficiently solvable parameterized enumeration problems. In this paper we focus on ordered enumeration and will show how to obtain Delay-FPT and Total-FPT enumeration algorithms for several important problems. We propose a generic algorithmic strategy, combining well-known principles stemming from both parameterized algorithmics and enumeration, which shows that, under certain preconditions, the existence of a so-called neighbourhood function among the solutions imp…

Fundamentals of Parameterized Complexity Revisited

Flum and Grohe define a parameter (parameterization) as a function $κ$ which maps words over a given alphabet to natural numbers. They require such functions to be polynomial-time computable. We show how this technical restriction can be lifted without breaking the theory. More specifically, instead of $κ$ we consider the set of languages that it bounds as parameterization and define the basic notions of parameterized complexity in terms of promise problems, which completely replace slices. One advantage of this formalization is that it becomes possible to interpret any complexity-theoretic co…

On the parameterized complexity of Compact Set Packing

The Set Packing problem is, given a collection of sets $\mathcal{S}$ over a ground set $\mathcal{U}$, to find a maximum collection of sets that are pairwise disjoint. The problem is among the most fundamental NP-hard optimization problems that have been studied extensively in various computational regimes. The focus of this work is on parameterized complexity, Parameterized Set Packing (PSP): Given $r \in {\mathbb N}$, is there a collection $ \mathcal{S}' \subseteq \mathcal{S}: |\mathcal{S}'| = r$ such that the sets in $\mathcal{S}'$ are pairwise disjoint? Unfortunately, the problem is not fix…

极大公共子序列枚举的复杂性

The Complexity of Maximal Common Subsequence Enumeration

本文研究了极大公共子序列枚举问题的复杂性，证明了在多字符串间枚举的困难性并排除了输出多项式时间算法的可能性，同时通过参数化复杂性分析提供了规避该难处理性的结果。

Parameter Compilation

In resolving instances of a computational problem, if multiple instances of interest share a feature in common, it may be fruitful to compile this feature into a format that allows for more efficient resolution, even if the compilation is relatively expensive. In this article, we introduce a formal framework for classifying problems according to their compilability. The basic object in our framework is that of a parameterized problem, which here is a language along with a parameterization---a map which provides, for each instance, a so-called parameter on which compilation may be performed. Ou…

网络中缓存的参数化复杂度

Parameterized Complexity of Caching in Networks

本文通过参数化复杂度范式对网络缓存问题进行全面分析，填补了除一般NP-hardness外可处理性边界未知的空白，并确立了算法上下界以明确该问题变得可处理的具体条件。