Subexponential Parameterized Algorithms

Years and Authors of Summarized Original Work

• 2009; Alon, Lokshtanov, Saurabh

• 2013; Fomin, Villanger

• 2014; Drange, Fomin, Pilipczuk, Villanger

Problem Definition

A parameterized problem is a language $L \subseteq \varSigma ^{{\ast}}\times \mathbb{N}$, where $\varSigma$ is a fixed, finite alphabet. The second component is called the parameter of the problem. The central notion in parameterized complexity is the notion of fixed-parameter tractability (FPT). A parameterized problem L is called FPT if it can be determined in time f(k) ⋅ n^c whether or not (x, k) ∈ L, where $n =\vert (x,k)\vert$, f is a computable function depending only on k, and c is a constant independent of n and k. The complexity class containing all fixed-parameter tractable problems is called FPT.

While in the definition of class FPT, we are happy with any computable function f, from application perspective it is often desirable to have the asymptotic growth of fas slow as possible. Take as an example an FPT...