Maximizing minimum cycle bases intersection

Ylène Aboulfath (1) , Dimitri Watel (2, 3, 4) , Marc-Antoine Weisser (5, 6) , Thierry Mautor (1) , Dominique Barth (1)

1 DAVID - Données et algorithmes pour une ville intelligente et durable - DAVID
2 IP Paris - Institut Polytechnique de Paris
3 SAMOVAR - Services répartis, Architectures, MOdélisation, Validation, Administration des Réseaux
4 ENSIIE - Ecole Nationale Supérieure d'Informatique pour l'Industrie et l'Entreprise
5 CentraleSupélec
6 LISN - Laboratoire Interdisciplinaire des Sciences du Numérique

In this paper we consider the problem of, given a set of graphs with the same set of vertices, choosing a minimum cycle basis for each of these graphs such that the intersection of these bases has maximal size. We first prove this problem to be NP-complete, then prove its polynomiality for the special case of two graphs and study both the hardness of approximation and the parameterized complexity.

Domains: Data Structures and Algorithms [cs.DS]; Computational Complexity [cs.CC]

Ylène Aboulfath, Dimitri Watel, Marc-Antoine Weisser, Thierry Mautor, Dominique Barth. Maximizing minimum cycle bases intersection. 2022. ⟨hal-03851365⟩