  The paper develops a general framework for constrained clustering which is
based on the close connection of geometric clustering and diagrams. Various new
structural and algorithmic results are proved (and known results generalized
and unified) which show that the approach is computationally efficient and
flexible enough to pursue various conflicting demands.
  The strength of the model is also demonstrated practically on real-world
instances of the electoral district design problem where municipalities of a
state have to be grouped into districts of nearly equal population while
obeying certain politically motivated requirements.
