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The paper develops a general framework for constrained clustering which isbased on the close connection of geometric clustering and diagrams. Various newstructural and algorithmic results are proved (and known results generalizedand unified) which show that the approach is computationally efficient andflexible enough to pursue various conflicting demands.  The strength of the model is also demonstrated practically on real-worldinstances of the electoral district design problem where municipalities of astate have to be grouped into districts of nearly equal population whileobeying certain politically motivated requirements.

Constrained clustering via diagrams: A unified theory and its applications to electoral district design