Khai Van Tran
01.01.2022 – 31.12.2022
We study the algorithmic complexity of parametric submodular function minimization in the context of the Quickest Transshipment Problem, a fundamental problem in the field of flows over time.
In a recent development, new tools for the Discrete Newton method and kernelization techniques for parametric submodular function minimizations were created in order to optimize the time horizon in the context of the Quickest Transshipment Problem. The only known algorithm for Integral Quickest Transshipments is due to Hoppe and Tardos and in this context a parametric submodular function minimization occurs as well. In this project, we aim to develop novel algorithms that find Integral Quickest Transshipments and whose worst-case running is faster than previously known approaches by orders of magnitude.
 M. Schlöter, M. Skutella and K. V. Tran. “A Faster Algorithm for Quickest Transshipments via an Extended Discrete Newton Method”. In: Proc. of the 33rd Annual ACM-SIAM Symposium on Discrete Algorithms. SODA 2022.
 B. Hoppe and É. Tardos. “The Quickest Transshipment Problem”. In: Mathematics of Operations Research 25.1 (2000).
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