An introduction to multi-parameter complexity analysis of discrete problems

A notion of multi-parameter complexity analysis of a discrete problem as the determining of complexities of its subproblems over all possible combinations of constraints on key parameters is introduced, and a notion of a basis system of subproblems is defined. Basic theorems on the existence, uniqueness and finiteness of the basis system are established. As an illustration to this approach, some results on the 4-parameter complexity analysis of the open shop scheduling problem and of the connected list coloring problem are presented.