RESUME:
After a few introductory remarks on the "automatic" part of Automatic Differentiation (AD)
we will concentrate on the presentation of the Efficient Jacobian Accumulation (EJA) problem. Apart from being a nice "playground" for graph theory, combinatorial optimization and complexity analysis its solution has a very relevant impact on AD and its application to real-world problems. Unfortunately, the resulting speedup by factors of 3 and more can not be obtained in an entirely "automatic" fashion since the EJA problem is conjectured to be NP-complete. Optimized elimination sequences will be used to generate efficient Jacobian code automatically. The above should be seen in the context of a more general next generation AD tool first ideas on which will be presented as an outlook.