Optimal Jacobian accumulation is NP-complete

@article{Naumann2008OptimalJA,
  title={Optimal Jacobian accumulation is NP-complete},
  author={Uwe Naumann},
  journal={Mathematical Programming},
  year={2008},
  volume={112},
  pages={427-441}
}
  • U. Naumann
  • Published 30 November 2007
  • Mathematics
  • Mathematical Programming
We show that the problem of accumulating Jacobian matrices by using a minimal number of floating-point operations is NP-complete by reduction from Ensemble Computation. The proof makes use of the fact that, deviating from the state-of-the-art assumption, algebraic dependences can exist between the local partial derivatives. It follows immediately that the same problem for directional derivatives, adjoints, and higher derivatives is NP-complete, too. 
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