  We devise a constant-factor approximation algorithm for the maximization
version of the edge-disjoint paths problem if the supply graph together with
the demand edges form a planar graph. By planar duality this is equivalent to
packing cuts in a planar graph such that each cut contains exactly one demand
edge. We also show that the natural linear programming relaxations have
constant integrality gap, yielding an approximate max-multiflow min-multicut
theorem.
