Refined notions of parameterized enumeration kernels with applications to matching cut enumeration

An enumeration kernel as defined by Creignou et al. (2017) [11] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of t...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 123; pp. 76 - 102
Main Authors: Golovach, Petr A., Komusiewicz, Christian, Kratsch, Dieter, Le, Van Bang
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2022
Subjects:
Enumeration problems
Kernelization
Matching cuts
Output-sensitive algorithms
Polynomial delay
Structural parameterizations
Enumeration problems
Output-sensitive algorithms
Polynomial delay
Structural parameterizations
Kernelization
Matching cuts
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary:An enumeration kernel as defined by Creignou et al. (2017) [11] for a parameterized enumeration problem consists of an algorithm that transforms each instance into one whose size is bounded by the parameter plus a solution-lifting algorithm that efficiently enumerates all solutions from the set of the solutions of the kernel. We propose to consider two new versions of enumeration kernels by asking that the solutions of the original instance can be enumerated in polynomial time or with polynomial delay from the kernel solutions. Using the NP-hard Matching Cut problem parameterized by structural parameters such as the vertex cover number or the cyclomatic number of the input graph, we show that the new enumeration kernels present a useful notion of data reduction for enumeration problems which allows to compactly represent the set of feasible solutions.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2021.07.005