BibTeX
@INPROCEEDINGS{
         Martens2025SJC,
       author = "Simon Martens and Uwe Naumann",
       title = "Scheduled {J}acobian Chaining",
       booktitle = "2025 Proceedings of the Conference on Applied and Computational Discrete
         Algorithms (ACDA), July~30--August~1, 2025",
       editor = "A. Conway and A. Pothen and M. Farach-Colton and B. U{\c{c}}ar",
       pages = "90--100",
       address = "Philadelphia, PA, USA",
       publisher = "SIAM",
       url = "https://doi.org/10.1137/1.9781611978759.7",
       doi = "10.1137/1.9781611978759.7",
       abstract = "This paper addresses the efficient computation of Jacobian matrices for programs
         composed of sequential differentiable subprograms. By representing the overall Jacobian as a chain
         product of the Jacobians of these subprograms, we reduce the problem to optimizing the sequence of
         matrix multiplications, known as the Jacobian Matrix Chain Product problem. Solutions to this
         problem yield ``optimal bracketings'', which induce a precedence-constraint scheduling
         problem. We investigate the inherent parallelism in the solutions and develop a new dynamic
         programming algorithm as a heuristic that incorporates the scheduling. To assess its performance, we
         benchmark it against the global optimum, which is computed via a branch-and-bound algorithm.",
       year = "2025",
       ad_theotech = "Combinatorics"
}