Parameterised Enumeration for Modification Problems

Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class DelayFPT 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 sh...

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Published in:	Algorithms Vol. 12; no. 9; p. 189
Main Authors:	Creignou, Nadia, Ktari, Raïda, Meier, Arne, Müller, Julian-Steffen, Olive, Frédéric, Vollmer, Heribert
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01.09.2019 MDPI
Subjects:	Algorithms Artificial Intelligence bounded search tree Complexity theory Computational Complexity Computer Science Context Discrete Mathematics Enumeration Logic in Computer Science ordering parameterised complexity parameterised enumeration Parameterization Parameterised Enumeration Bounded Search Tree Parameterised complexity
ISSN:	1999-4893, 1999-4893
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Abstract	Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class DelayFPT 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.
AbstractList	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 Recently, Creignou et al. (Theory Comput. Syst. 2017), introduced the class DelayFPT 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.
Author	Vollmer, Heribert Creignou, Nadia Meier, Arne Olive, Frédéric Müller, Julian-Steffen Ktari, Raïda
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SubjectTerms	Algorithms Artificial Intelligence bounded search tree Complexity theory Computational Complexity Computer Science Context Discrete Mathematics Enumeration Logic in Computer Science ordering parameterised complexity parameterised enumeration Parameterization
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Title	Parameterised Enumeration for Modification Problems
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