Parameterised Enumeration for Modification Problems

Nadia Creignou (1) , Raïda Ktari (2) , Arne Meier (3) , Julian-Steffen Müller (3) , Frédéric Olive (1) , Heribert Vollmer (3)

1 LIRICA - Logique, Interaction, Raisonnement et Inférence, Complexité, Algèbre
2 ISIMS - Institut Supérieur d'Informatique et de Multimédia de Sfax
3 Leibniz Universität Hannover=Leibniz University Hannover

Recently, Creignou et al. (Theory Comput. Syst. 2017) have introduced the class 1 DelayFPT into parameterised complexity theory in order to capture the notion of efficiently solvable 2 parameterised enumeration problems. In this paper, we propose a framework for parameterised 3 ordered enumeration and will show how to obtain enumeration algorithms running with an FPT delay 4 in the context of general modification problems. We study these problems considering two different 5 orders of solutions, namely, lexicographic order and order by size. Furthermore, we present two 6 generic algorithmic strategies. The first one is based on the well-known principle of self-reducibility 7 and is used in the context of lexicographic order. The second one shows that the existence of a 8 neighbourhood structure among the solutions implies the existence of an algorithm running with 9 FPT delay which outputs all solutions ordered non-decreasingly by their size. 10

Mots clés: Parameterised complexity; Enumeration; Bounded Search Tree; Parameterised

Domaines: Complexité [cs.CC]; Intelligence artificielle [cs.AI]; Mathématique discrète [cs.DM]; Logique en informatique [cs.LO]

Nadia Creignou, Raïda Ktari, Arne Meier, Julian-Steffen Müller, Frédéric Olive, et al.. Parameterised Enumeration for Modification Problems. Algorithms, 2019, 12 (9), pp.189. ⟨10.3390/a12090189⟩. ⟨hal-02439368⟩