Enumerating minimal connected dominating sets in graphs of bounded chordality

Enumerating objects of specified type is one of the principal tasks in algorithmics. In graph algorithms one often enumerates vertex subsets satisfying a certain property. We study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chorda...

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Bibliographic Details
Published in:Theoretical computer science Vol. 630; pp. 63 - 75
Main Authors: Golovach, Petr A., Heggernes, Pinar, Kratsch, Dieter
Format: Journal Article
Language:English
Published: Elsevier B.V 30.05.2016
Elsevier
Subjects:
Algorithms
Automatic
Engineering Sciences
Enumeration
Exact exponential algorithms
Graph theory
Graphs
Minimal connected dominating sets
Tasks
Upper bounds
Exact exponential algorithms
Minimal connected dominating sets
Enumeration
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary:Enumerating objects of specified type is one of the principal tasks in algorithmics. In graph algorithms one often enumerates vertex subsets satisfying a certain property. We study the enumeration of all minimal connected dominating sets of an input graph from various graph classes of bounded chordality. We establish enumeration algorithms as well as lower and upper bounds for the maximum number of minimal connected dominating sets in such graphs. In particular, we present algorithms to enumerate all minimal connected dominating sets of chordal graphs in time O(1.7159n), of split graphs in time O(1.3803n), and of AT-free, strongly chordal, and distance-hereditary graphs in time O⁎(3n/3), where n is the number of vertices of the input graph. Our algorithms imply corresponding upper bounds for the number of minimal connected dominating sets for these graph classes.
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2016.03.026