eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2015-11-19
307
318
10.4230/LIPIcs.IPEC.2015.307
article
Enumerating Minimal Connected Dominating Sets in Graphs of Bounded Chordality
Golovach, Petr A.
Heggernes, Pinar
Kratsch, Dieter
Listing, generating or 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(1.7159^n), of split graphs in time O(1.3803^n), and of AT-free, strongly chordal, and distance-hereditary graphs in time O^*(3^{n/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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol043-ipec2015/LIPIcs.IPEC.2015.307/LIPIcs.IPEC.2015.307.pdf
Minimal connected dominating set
exact algorithms
enumeration