Abstract
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| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) and the space complexity is O(|V| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), 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
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