Power Edge Set and Zero Forcing Set Remain Difficult in Cubic Graphs

Pierre Cazals (1) , Benoit Darties (2) , Annie Chateau (3) , Rodolphe Giroudeau (2) , Mathias Weller (4, 5)

1 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision
2 MAORE - Methods, Algorithms for Operations REsearch
3 MAB - Méthodes et Algorithmes pour la Bioinformatique
4 CNRS - Centre National de la Recherche Scientifique
5 LIGM - Laboratoire d'Informatique Gaspard-Monge

This paper presents new complexity and non-approximation results concerning two color propagation problems, namely Power Edge Set and Zero Forcing Set. We focus on cubic graphs, exploiting their structural properties to improve and refine previous results. We also give hardness results for parameterized precolored versions of these problems, and a polynomial-time algorithm for Zero Forcing Set in proper interval graphs.

Mots clés: Synchrophasor; Power Edge Set; Zero Forcing Set; Complexity

Domaines: Complexité [cs.CC]; Algorithme et structure de données [cs.DS]

Pierre Cazals, Benoit Darties, Annie Chateau, Rodolphe Giroudeau, Mathias Weller. Power Edge Set and Zero Forcing Set Remain Difficult in Cubic Graphs. IWOCA 2019 - 30th International Workshop on Combinatorial Algorithms, Jul 2019, Pisa, Italy. pp.122-135, ⟨10.1007/978-3-030-25005-8_11⟩. ⟨hal-02359076⟩