On Happy Colorings, Cuts, and Structural Parameterizations

We study the Maximum Happy Vertices and MaximumHappy Edges problems. The former problem is a variant of clusterization, where some vertices have already been assigned to clusters. The second problem gives a natural generalization of Multiway Uncut, which is the complement of the classical Multiway C...

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Bibliographic Details
Published inGraph-Theoretic Concepts in Computer Science Vol. 11789; pp. 148 - 161
Main Authors Bliznets, Ivan, Sagunov, Danil
Format Book Chapter
LanguageEnglish
Published Switzerland Springer International Publishing AG 01.01.2019
Springer International Publishing
SeriesLecture Notes in Computer Science
Subjects
Clique-width
Distance to triviality
Happy coloring
Homophily law
Maximum happy edges
Maximum happy vertices
Multiway cut
Parameterized complexity
Treewidth
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Summary:We study the Maximum Happy Vertices and MaximumHappy Edges problems. The former problem is a variant of clusterization, where some vertices have already been assigned to clusters. The second problem gives a natural generalization of Multiway Uncut, which is the complement of the classical Multiway Cut problem. Due to their fundamental role in theory and practice, clusterization and cut problems has always attracted a lot of attention. We establish a new connection between these two classes of problems by providing a reduction between Maximum Happy Vertices and Node Multiway Cut. Moreover, we study structural and distance to triviality parameterizations of Maximum Happy Vertices and Maximum Happy Edges. Obtained results in these directions answer questions explicitly asked in four works: Agrawal ’17, Aravind et al. ’16, Choudhari and Reddy ’18, Misra and Reddy ’17.
Bibliography:This research was supported by the Russian Science Foundation (project 16-11-10123).
ISBN:9783030307851
3030307859
ISSN:0302-9743
1611-3349
DOI:10.1007/978-3-030-30786-8_12