Exact Graph Coloring for Functional Decomposition: Do We Need It?

| Finding column multiplicity index is one of important component processes in functional decomposition of discrete functions for circuit design and especially Data Mining applications. How important it is to solve this problem exactly from the point of view of the minimum complexity of decomposition, and related to it error in Machine Learning type of applications? In order to investigate this problem we wrote two graph coloring programs: exact program EXOC and approximate program DOM (DOM can give provably exact results on some types of graphs). These programs were next incorporated into the multi-valued decomposer of functions and relations MVGUD. Extensive testing of MVGUD with these programs has been performed on various kinds of data. Based on these tests we demonstrated that exact graph coloring is not necessary for high-quality functional decomposers, especially in Data Mining applications, giving thus another argument that eecient and eeective Machine Learning approach based on decomposition is possible.