Parameterized Enumeration for Modification Problems

Recently the class \(DelayFPT\) has been introduced into parameterized complexity in order to capture the notion of efficiently solvable parameterized enumeration problems. In this paper we propose a framework for parameterized ordered enumeration and will show how to obtain \(DelayFPT\) enumeration algorithms in the context of graph modification problems. We study these problems considering two different orders of solutions, lexicographic and by size. We present generic algorithmic strategies: The first one is based on the well-known principle of self-reducibility in the context of lexicographic order. The second one shows that the existence of some neighborhood structure among the solutions implies the existence of a \(DelayFPT\) algorithm which outputs all solutions ordered non-decreasingly by their size.