Model-based construction of Open Non-uniform Cylindrical Algebraic   Decompositions
  In this paper we introduce the notion of an Open Non-uniform Cylindrical Algebraic Decomposition (NuCAD), and present an efficient model-based algorithm for constructing an Open NuCAD from an input formula. A NuCAD is a generalization of Cylindrical Algebraic Decomposition (CAD) as defined by Collins in his seminal work from the early 1970s, and as extended in concepts like Hong's partial CAD. A NuCAD, like a CAD, is a decomposition of n-dimensional real space into cylindrical cells. But unlike a CAD, the cells in a NuCAD need not be arranged cylindrically. It is in this sense that NuCADs are not uniformly cylindrical. However, NuCADs--- like CADs --- carry a tree-like structure that relates different cells. It is a very different tree but, as with the CAD tree structure, it allows some operations to be performed efficiently, for example locating the containing cell for an arbitrary input point. 
Christopher W. Brown
cs.SC