  We consider the capacitated domination problem, which models a
service-requirement assigning scenario and which is also a generalization of
the dominating set problem. In this problem, we are given a graph with three
parameters defined on the vertex set, which are cost, capacity, and demand. The
objective of this problem is to compute a demand assignment of least cost, such
that the demand of each vertex is fully-assigned to some of its closed
neighbours without exceeding the amount of capacity they provide.
  In this paper, we provide the first constant factor approximation for this
problem on planar graphs, based on a new perspective on the hierarchical
structure of outer-planar graphs. We believe that this new perspective and
technique can be applied to other capacitated covering problems to help tackle
vertices of large degrees.
