Before revision:  More precisely, an instance of this problem consists of (i) a planar graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of the plane given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise non-intersecting "pipes" corresponding to the bundles, connecting certain pairs of these discs.
After revision:  More precisely, an instance of this problem consists of (i) a planar graph G whose vertices are partitioned into clusters and whose inter-cluster edges are partitioned into bundles, and (ii) a region R of a 2-dimensional compact surface M given as the union of a set of pairwise disjoint discs corresponding to the clusters and a set of pairwise non-intersecting "pipes" corresponding to the bundles, connecting certain pairs of these discs.