Crosstalk-constrained maze routing based on Lagrangian relaxation

With the increasing density of VLSI circuits, interconnection wires are getting packed even closer. This has increased the effect of interaction between wires on circuit performance and hence, the importance of controlling crosstalk. Maze routing is a robust and general approach which can be used in many situations including multi-layer interconnections. In this paper we consider crosstalk avoidance in maze routing. The crosstalk-constrained maze routing problem is first formulated. Then we show it is equivalent to the multi-constrained shortest path problem and is strongly NP-complete. Based on the Lagrangian relaxation technique, an effective heuristic algorithm is designed to solve the problem.