Direction-Constrained Rectangle Escape Routing

Abstract

Given a set of buses with available escape directions inside a chip, a two-phase algorithm is proposed to assign one feasible escape direction onto any bus such that the number of used layers is minimized and to allocate the pin rectangle and the projection rectangle of any escape bus onto the minimized layers in direction-constrained rectangle escape routing. In our proposed algorithm, based on the concept of two-dimensional maximum density inside a chip, the escape directions of the buses can be first assigned to minimize the number of the used layers by iteratively eliminating unnecessary escape directions for any bus inside a chip. Furthermore, based on the construction of the represented intervals and the assignment constraints for the escape buses, a modified left-edge algorithm can be used to allocate all the escape buses onto the minimized layers. Compared with Ma’s integer linear program (ILP)-based algorithm [10] using lp_solve and Gurobi in rectangle escape routing, the experimental results show that our proposed algorithm obtains the same results but reduces CPU time by 94.2% and 35.7% when using lp_solve and Gurobi for 16 tested examples with no direction constraint on average, respectively. Compared with the modified algorithm from Ma's ILP-based algorithm [10] using lp_solve and Gurobi in direction-constrained rectangle escape routing, the experimental results show that our proposed algorithm obtains the same results but reduces CPU time by 94.3% and 37.7% when using lp_solve and Gurobi for 16 tested examples with direction constraints on average, respectively. Besides that, compared with Yan’s iterative algorithm, the experimental results show that our proposed algorithm increases CPU time by 1.0% to reduce the number of used layers 11.1% for 16 tested examples on average.