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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Bibliographic Details
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
Online Access:Get full text
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Summary: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.
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ISSN:1999-4893
1999-4893
DOI:10.3390/a12090189