A new graph coloring algorithm for constrained via minimization

This paper proposes a new layer assignment algorithm for constrained via minimization in VLSI chip design. The new algorithm uses an intersect graph model and applies a pseudo two coloring technique in order to find near optimal layer assignments in two layers. The pseudo two coloring problem is known to be NP-complete in the general case but a polynomial solution exists for planar graphs. This paper compares the proposed algorithm to optimal results produced in planar and nonplanar graphs as well as to another recent two coloring heuristic in random graphs. The paper also discusses the possibility of extending the algorithm to mutilayers.