Study of Identifying Code Polyhedra for Some Families of Split Graphs

Gabriela Argiroffo , Silvia Bianchi (1) , Annegret K Wagler (2)

1 UNINE - Université de Neuchâtel = University of Neuchatel
2 LIMOS - Laboratoire d'Informatique, de Modélisation et d'Optimisation des Systèmes

The identifying code problem is a newly emerging search problem, challenging both from a theoretical and a computational point of view, even for special graphs like bipartite graphs and split graphs. Hence, a typical line of attack for this problem is to determine minimum identifying codes of special graphs or to provide bounds for their size. In this work we study the associated polyhedra for some families of split graphs: headless spiders and complete suns. We provide the according linear relaxations, discuss their combinatorial structure, and demonstrate how the associated polyhedra can be entirely described or polyhedral arguments can be applied to find minimum identifying codes for special split graphs. We discuss further lines of research in order to apply similar techniques to obtain strong lower bounds stemming from linear relaxations of the identifying code polyhedron, enhanced by suitable cutting planes to be used in a B&C framework.

Mots clés: identifying code problem; polyhedral approach; split graphs

Domaines: Mathématique discrète [cs.DM]

Gabriela Argiroffo, Silvia Bianchi, Annegret K Wagler. Study of Identifying Code Polyhedra for Some Families of Split Graphs. Combinatorial Optimization. ISCO 2014, Fouilhoux P., Gouveia L., Mahjoub A., Paschos V. (eds), pp.13-25, 2014. ⟨hal-02045768⟩