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An Efficient Algorithm for Power Dominating Set

Bläsius, Thomas ORCID iD icon 1; Göttlicher, Max 1; Gørtz, Inge Li [Hrsg.]; Farach-Colton, Martin [Hrsg.]; Puglisi, Simon J. [Hrsg.]; Herman, Grzegorz [Hrsg.]
1 Institut für Theoretische Informatik (ITI), Karlsruher Institut für Technologie (KIT)

Abstract:

The problem Power Dominating Set (PDS) is motivated by the placement of phasor measurement units to monitor electrical networks. It asks for a minimum set of vertices in a graph that observes all remaining vertices by exhaustively applying two observation rules. Our contribution is twofold. First, we determine the parameterized complexity of PDS by proving it is W[P]-complete when parameterized with respect to the solution size. We note that it was only known to be W[2]-hard before. Our second and main contribution is a new algorithm for PDS that efficiently solves practical instances.
Our algorithm consists of two complementary parts. The first is a set of reduction rules for PDS that can also be used in conjunction with previously existing algorithms. The second is an algorithm for solving the remaining kernel based on the implicit hitting set approach. Our evaluation on a set of power grid instances from the literature shows that our solver outperforms previous state-of-the-art solvers for PDS by more than one order of magnitude on average. Furthermore, our algorithm can solve previously unsolved instances of continental scale within a few minutes.


Verlagsausgabe §
DOI: 10.5445/IR/1000163538
Veröffentlicht am 27.10.2023
Originalveröffentlichung
DOI: 10.4230/lipics.esa.2023.21
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Theoretische Informatik (ITI)
Publikationstyp Proceedingsbeitrag
Publikationsjahr 2023
Sprache Englisch
Identifikator ISBN: 978-3-9597729-5-2
ISSN: 1868-8969
KITopen-ID: 1000163538
Erschienen in 31st Annual European Symposium on Algorithms (ESA 2023). Hrsg.: I., Li Gortz; M., Farach-Colton; S.J., Puglisi; G., Herman
Veranstaltung 31st 31st Annual European Symposium on Algorithms (Part of ALGO 2023) (ESA 2023), Amsterdam, Niederlande, 04.09.2023 – 08.09.2023
Verlag Schloss Dagstuhl - Leibniz-Zentrum für Informatik (LZI)
Seiten 1-15
Serie Leibniz International Proceedings in Informatics (LIPIcs) ; 274
Schlagwörter Power Dominating Set, Implicit Hitting Set, Parameterized Complexity, Reduction Rules
Nachgewiesen in Scopus
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