Optimal jumper insertion for antenna avoidance under ratio upper-bound

Antenna effect may damage gate oxides during plasma-based fabrication process. The antenna ratio of total exposed antenna area to total gate oxide area is directly related to the amount of damage. Jumper insertion is a common technique applied at routing and post-layout stages to avoid and to fix the problems caused by the antenna effect. This paper presents an optimal algorithm for jumper insertion under the ratio upper-bound. It handles Steiner trees with obstacles. The algorithm us based on dynamic programming while works on free trees. The time complexity is O(alpha|V|
²
) and the space complexity is O(|V|
²
), where |V| is the number of nodes in the routing tree and a is a factor depending on how to find a non-blocked position on a wire for a jumper