Your rugby mates don't need to know your colleagues: Triadic closure with edge colors

Laurent Bulteau (1) , Niels Grüttemeier , Christian Komusiewicz , Manuel Sorge

1 LIGM - Laboratoire d'Informatique Gaspard-Monge

Given an undirected graph G = (V , E) the NP-hard Strong Triadic Closure (STC) problem asks for a labeling of the edges as weak and strong such that at most k edges are weak and for each induced P 3 in G at least one edge is weak. We study the following generalizations of STC with c different strong edge colors. In Multi-STC an induced P 3 may receive two strong labels as long as they are different. In Edge-List Multi-STC and Vertex-List Multi-STC we may restrict the set of permitted colors for each edge of G. We show that, under the Exponential Time Hypothesis (ETH), Edge-List Multi-STC and Vertex-List Multi-STC cannot be solved in time 2 o(|V | 2). We proceed with a parameterized complexity analysis in which we extend previous algorithms and kernelizations for STC [11,14] to the three variants or outline the limits of such an extension.

Domaines: Complexité [cs.CC]; Bio-informatique [q-bio.QM]; Algorithme et structure de données [cs.DS]

Laurent Bulteau, Niels Grüttemeier, Christian Komusiewicz, Manuel Sorge. Your rugby mates don't need to know your colleagues: Triadic closure with edge colors. Journal of Computer and System Sciences, 2021, 120, pp.75 - 96. ⟨10.1016/j.jcss.2021.03.001⟩. ⟨hal-03388392⟩