Dual graph contraction for irregular pyramids

A new algorithm for building irregular pyramids is presented. The algorithm is based on only two basic operations on graphs, contraction and removal of edges. By making use of the concept of dual graphs, the algorithm overcomes the problem of unbounded vertex degree proper to the existing approach to building irregular pyramids. This boundedness extends the scope of parallel, degree preserving graph contraction also to irregular structures. Our method can be applied to all problems in which a 2D discrete space can be represented by a planar graph. Four-connected square grids, region adjacency graphs, Voronoi diagrams and Delaunay triangulations are examples of such plane representations