λ-geometry clock tree construction with wirelength and via minimization

λ-geometry routing provides more available routing directions on different metal layers for chip interconnection to reduce wirelength. However, it can lead to a significant increase in via cost. In this paper, we consider lambda-geometry zero-skew clock tree construction with wirelength and via minimization. Our lambda-geometry clock router achieves, on average, a 7.57% wirelength reduction in the Y-architecture and 9.68% in the X-architecture when compared with results in the Manhattan architecture. In addition, we also propose a dynamic programming approach to determine the one-bend routes of the clock edges to optimize the total node via cost of the whole clock tree. Our via minimization algorithm can reduce the total via cost by an average of 17% in the Y-architecture and 37% in the X architecture.