Y-architecture-based flip-chip routing with dynamic programming-based bend minimization

In modern VLSI designs, I/O counts have been growing continuously as the system becomes more complicated. To achieve higher routability, the hexagonal array is introduced with higher pad density and a larger pitch. However, the routing for hexagonal arrays is significantly different from that for traditional gird and staggered arrays. In this paper, we consider the Y-architecture-based flip-chip routing used for the hexagonal array. Unlike the conventional Manhattan and the X-architectures, the Y-architecture allows wires to be routed in three directions, namely, 0-, 60-, and 120-degrees. We first analyze the routing properties of the hexagonal array. Then, we propose a triangular tile model and a chord-based internal node division method that can handle both pre-assignment and free-assignment nets without wire crossing. Finally, we develop a novel dynamic programming-based bend minimization method to reduce the number of routing bends in the final solution. Experimental results show that our algorithm can achieve 100% routability with minimized total wirelength and the number of routing bends effectively.