An improved column compatibility approach for partition based functional decomposition

The paper deals with the problem of generating compatible pairs of a k-block partition P(B)=(B₁, B₂, ..., B_k ), where B is the bound set. Compatible and incompatible pairs of block partitions of P(B) are generated by a partition calculus based approach called the Block Compatible Approach. The compatible block partitions generate a compatibility graph that can be solved using clique partition algorithms. The incompatible block partitions form an incompatibility graph, which can be solved using a graph colouring algorithm or maximum independent set (MIS) partition algorithm