Solving the Pricing Problem in a Branch-and-Price Algorithm for Graph Coloring Using Zero-Suppressed Binary Decision Diagrams

Branch-and-price algorithms combine a branch-and-bound search with an exponentiallysized LP formulation that must be solved via column generation. Unfortunately, the standard branching rules used in branch-and-bound for integer programming interfere with the structure of the column generation routine; therefore, most such algorithms employ alternate branching rules to circumvent this difficulty. This paper shows how a zero-suppressed binary decision diagram (ZDD) can be used to solve the pricing problem for a generic branch-and-price algorithm, even in the presence of constraints imposed by branching decisions. This approach facilitates a much more direct solution method, and can improve convergence of the column generation subroutine. Computational results are presented showing the effectiveness of this method for the graph coloring problem.