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Parameterised Enumeration for Modification Problems

1
Aix-Marseille Université, CNRS, LIS, 13003 Marseille, France
2
Pôle technologique de Sfax, Université de Sfax, Sfax 3000, Tunisia
3
Institut für Theoretische Informatik, Leibniz Universität Hannover, 30167 Hannover, Germany
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Author to whom correspondence should be addressed.
This paper is an extended version of our paper published in Parameterized Enumeration for Modification Problems. In Proceedings of the Language and Automata Theory and Applications—9th International Conference, Nice, France, 2–6 March 2015
Algorithms 2019, 12(9), 189; https://doi.org/10.3390/a12090189
Received: 14 July 2019 / Revised: 29 August 2019 / Accepted: 5 September 2019 / Published: 9 September 2019
(This article belongs to the Special Issue New Frontiers in Parameterized Complexity and Algorithms)
Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class Delay FPT into parameterised complexity theory in order to capture the notion of efficiently solvable parameterised enumeration problems. In this paper, we propose a framework for parameterised ordered enumeration and will show how to obtain enumeration algorithms running with an FPT delay in the context of general modification problems. We study these problems considering two different orders of solutions, namely, lexicographic order and order by size. Furthermore, we present two generic algorithmic strategies. The first one is based on the well-known principle of self-reducibility and is used in the context of lexicographic order. The second one shows that the existence of a neighbourhood structure among the solutions implies the existence of an algorithm running with FPT delay which outputs all solutions ordered non-decreasingly by their size.
Keywords: parameterised complexity; enumeration; bounded search tree; parameterised enumeration; ordering parameterised complexity; enumeration; bounded search tree; parameterised enumeration; ordering
MDPI and ACS Style

Creignou, N.; Ktari, R.; Meier, A.; Müller, J.-S.; Olive, F.; Vollmer, H. Parameterised Enumeration for Modification Problems. Algorithms 2019, 12, 189.

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