The hardness of routing two pairs on one face

Guyslain Naves (1)

1 G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production

We prove the NP-completeness of the integer multiflow problem in planar graphs, with the following restrictions: there are only two edges of demand, both lying on the infinite face of the routing graph. It solves a question from Müller. We also give a directed version with only two terminals, and a directed acyclic version, both we only two arcs of demand.

Mots clés: integer multiflows; planar graphs; disjoint paths; NP-completeness

Domaines: Mathématique discrète [cs.DM]

Guyslain Naves. The hardness of routing two pairs on one face. 2008. ⟨hal-00313944v1⟩